Safe & Sounded - DIO, The International Journal of ... · of heliocentrist astronomers: DIO 1.1 z1...

Vol. 9 No. 1 1999 June ISSN 1041-5440

DIODIO 9.1 Established French Planet Priority: Scientific American Dec.2004

Recovery of theRGO Neptune Papers:

Safe & Sounded

Ecliptical Traces BeneathHipparchos’ Commentary

Aristarchos’ Precession:150 Years Before Hipparchos

2 1999 June DIO 9.1

Table of Contents Page:

‡1 British Neptune-Disaster File Recovered [2011 Update: www.dioi.org/nap.htm] 3‡2 Ecliptical Coordinates Beneath Hipparchos’ Commentary by K. PICKERING 26‡3 Cont’d-Fraction Decipherment: Ancestry of Ancient Yearlengths & Precession 30

News NotesAlex Jones’ Unique Discovery:

As we go to press with this issue, we learn that Alex Jones1 (the most honest andself-assured of all professional specialists in ancient astronomy) is publishing through theAmerican Philosophical Society (APS Memoirs vol. 233; 1999) a sensational find: the firstextant raw Greek astronomical observation2 from the 2nd century AD not coming throughPtolemy. Alex discovered the papyrus containing this wholly unexpected treasure in theOxyrhynchus collection. This papyrus is not just the first of its kind — it may remainforever the sole surviving example of its kind.

Moreover, the document in which it is embedded (very possibly by Menelaos!) containsserious astronomy — relevant to checking (by observation) planetary period-relations of thesort discussed3 in DIO as preferable to Ptolemy’s approach. Jones recognizes the differenceand politely4 cites the views of R. Newton, G. Toomer, and DR on this issue.

The document appears to be a rare window into the long-“lost” period between Hip-parchos and Ptolemy, hopefully a glimpse of real astronomers at work deriving their oftenimpressively accurate5 orbital parameters, not by neat geometric proofs from a minimalnumber of data (as indoor-mathematician Ptolemy presented things, after appropriatingthese astronomers’ parameters) but by repeated laborious and meticulous celestial observa-tions, which (long before Gauss) scrupulously ensured their orbits’ reliability by generousobservational overdetermination (fn 3). Who would have expected such a shocker fromoriginal Greek papyri? (Even from the Oxyrhynchus collection.) This discovery alone (andthere will be others) ensures Jones’ recognition as one of the great figures in our field.

The Ptolemy Debate:O.Gingerich & J.Evans finally agreed to a debate on Ptolemy (U.Notre Dame, 99/7/3),

once assured ogre DR would not be on the skeptical team. (Which was: DIO’s K.Pickering& H.Thurston.) DIO will print all debate papers submitted here. Evans had long refused toanswer Thurston’s polite written questions on the amusing Evans star-magnitude problemsnoted at DIO 4.1 ‡4 (& DIO 8 News Notes, sent to Evans, who trashcanned the wholeissue without reading it). So DR asked these questions from the floor; but we still haveno numbers from Evans. Urging live conversation & mutual understanding, DR afterwardsasked Evans (former massive DR-attacker: 64pp in 1987 JHA!) for his phone number, homeor office. He refused both requests.

The debate was so one-sided that it wasn’t even necessary to bring in DR’s surprise“Magnitude-Split” test [at www.dioi.org/cot.htm#msmr], which uses the major deep-southstars of any historical catalog to determine whether it was incomplete or the observer’ssouthern horizon was blocked. If neither, the test easily finds his latitude and epoch.

1[Note added 2015. Jones now at NYU. On his integrity since joining JHA, see DIO 16 ‡3.]2Jupiter near opposition in Cnc, 104/12/31 — observed to verify an accurate period relation of

344 sidereal years, comparing the observation to a −240 observation of Jupiter by the Dionysians(from whom this journal partly draws its name, since it appears that this was the earliest known groupof heliocentrist astronomers: DIO 1.1 ‡1 §D2). The 104 datum is presumably part of a series ofobservations of Jupiter’s entire retrograde-loop replay of its 241 BC behavior.

3 DIO 1.2 fn 78 & DIO 6 fn 51.4One of the many delightful ironies of the Ptolemy affair is watching the youngest able scholar in

the field — teaching good manners to all his elders.5Queen’s Qrtly 91:969, Vistas in Astron 28:255, AmJPhys 55:239 n.30 (vs DIO 11.2 cover) & n.38.

1999 June DIO 9.1 3

‡1 British Neptune-Disaster File RecoveredNOAO-DIO Preservation Project Succeeds

Long-Hidden RGO File on 1846 Planet-Chase: Safe At LastAdams’ Final Prediction Missed by Over Ten Degrees

Britain’s “Discoverer”: Perfect Simp or Conniving Babe?

French mathematical astronomer Urbain Leverrier’s amazing 1846/9/23 discovery ofthe giant planet Neptune “with the point of his pen”1 is the grandest legend in the long historyof astronomy. From tiny, nearly invisible deviations in the orbit of Uranus, he induced byrefined gravitational mathematics the position of Uranus’ perturber — the then-unknownplanet Neptune — and published its celestial longitude in the journal of the French Academyon 1846/8/31; 23 days later, Neptune was found telescopically at the Berlin Observatory,upon Leverrier’s written request, within one degree of the very spot predicted.

Leverrier’s success culminated a year of the most delicate and intensive mathemati-cal labor (starting no later than 1845 Sept); but his 1846 glory was immediately sulliedby a peculiar, entirely post-discovery-published claim of prior prediction by Universityof Cambridge mathematician John Couch Adams, a claim publicly backed by the ultimoAstronomer Royal, Geo. Airy. Over a century later, the Adams claim became even ichthier:soon after DR asked (1967-1969) Airy’s modern successor as Astronomer Royal for per-mission to examine the British file on the case, the whole file was “stolen”. We will callthis long-gone key resource the “RGON” (Royal Greenwich Observatory’s Neptune) file.

DIO was the first (and is still the only) journal to reveal (1992 & 1994) that the “thief”2

was in truth the then-recent Chief Ass’t to the Astronomer Royal, Australian RichardWoolley, and was Woolley’s closest professional confidante (who had by this time becomeDirector of Australia’s Mt. Stromlo Observatory). All of which raised the obvious question:was the RGON file’s disappearance related to possibly-embarrassing contents? (Obviouspoint: no one person can protect a file from unrestricted access for a century and a half —yet the ultra-sensitive RGON file has been so sheltered.)

In late 1998, the former Chief Ass’t died. And, lo, the RGON file was found among hiseffects by Nick Suntzeff (NOAO), as DIO first learned from Owen Gingerich. (Gingerich,while recognizing the British establishment to be obsessively secretive, is going along withthat establishment’s position that the file’s longtime unavailability to historians was justan accident.) British scholars were very shy of talking about the matter, but several DIOprobes by phone gradually pieced together the situation sufficiently that we were able toapproach NOAO (National Optical Astronomy Observatories) with reliable knowledge thatthe longlost file now resided (in diplomatic limbo) at NOAO’s Chilean observatory.

Upon DIO’s detailed-fax 1999/4/29 appeal, NOAO extraordinarily xeroxed the filethere (Cerro Tololo) and sent three copies via diplomatic bag to NOAO headquarters in

1The just-right appreciation declared (Comptes Rendus 23:660; 1846/10/5), in the afterglow of themoment of discovery, by topflight physicist & Paris Observatory head F. Arago.

2 RGO defenders are saying he didn’t really steal. (If taking a unique, 32y-sought file for the rest ofyour long life isn’t theft, what is?) DIO holds (§L) that the Chief Ass’t (formerly OSS-CIA) didn’t takethe file on his own. This is disputed by establishmentarians largely on the ground that he took otherRGO material as well. But the timing (DB §C2) of & varying cover stories (DB §I1) for the removalof the ORIGINALS of the Neptune file AND (§L6) the RGO list of its contents (in a xerox era: compareDB §D10), smells like the old RGO’s wish to hide the messy truth underlying its Neptune-fumblingfarce. Whatever ingenious alibis & diversionary tactics are generated, the fact is: there’s been no otherdecade-long public call for any other entire missing RGO file. (A call begun not by DR but by freshRGO archivist Adam Perkins in 1987 and by Ian Ridpath, who wrote the 1988/1 Popular Astronomynotice quoted at DB §B.) In fairness to England, it should be noted that the former Chief Ass’t (thoughlong a high official in British and British Commonwealth astronomy) was born in the US, not the UK.[Note added 2003. He stole parts of Airy DSB entry verbatim from Airy autobio. More “accident”?]

4 Neptune File Saved, Adams Legend Lost 1999 June DIO 9.1 ‡1

Tucson, one to be kept at the NOAO library (Mary Guerrieri), two for transmission directlyfrom Tucson to DIO (Baltimore and Cal Tech branches: DR and Myles Standish, resp).

The NOAO effort was not in vain. The file’s contents throw crucial new light uponBritish maneuvering (before and after discovery) as well as the Univ Cambridge principals’fingerpointing after losing the planet to foreigners. Among the most remarkable newfinds: [a] From the outset, the Royal Greenwich Observatory (RGO) had inside knowledgeof Leverrier’s Uranus project (fn 69), [b] Airy privately hinted that he regarded Adams’generating post-discovery alibis (for not publishing his results) as “conniving” in falsehoods(§J8). [c] Adams is reported (§H11) to have been reluctant to publish his results even manyweeks after the discovery. [d] Adams’ very-little-known large error (about 12◦) in his finalpre-discovery prediction of Neptune’s place (a prior DIO revelation: §G1, Rawlins 1992Wfn 55) is specifically proven (and is the subject of a regretful explanation by Adams: §G3).

In the article that follows, unashamedly-ubiquitous references to our three previous DIOdiscussions of the Neptune affair (all published before the RGON file’s recent recovery)are merely intended to permit our readers’ efficiently-precise consultation of these detailedanalyses & data. For convenience, these publications will be abbreviated below as DA(Rawlins 1992W), DB (Rawlins 1994N), and DC (DIO 7.1 ‡5 §A).

Notes of Thanks:DIO’s fateful 1999/4/29 faxed request to NOAO, asking for the creation of a safety-

backup copy of this invaluable file — so long elusive and so often bowdlerized — wassupported by prominent interested parties, e.g., Cal Tech’s JPL (Myles Standish), UnivAlberta (Robert W. Smith), AAAS’ Science (Eliot Marshall), and the New York TimesScience Dep’t (Nicholas Wade). (Standish and Marshall followed up with valuable faxes oftheir own. They deserve much of the credit for success in this project — which came truelargely because we simply appealed to scientific institutions’ best ideals and intentions.)

To our mutual delight, the safety copy was indeed made. Thus, thanks to the responsive-ness and archival concern of NOAO, the RGON file has been firmly preserved for posterity.Astronomers’ gratitude must go in particular to Elaine MacAuliffe of NOAO’s Cerro TololoObservatory (Chile), who swiftly accomplished a task3 not only arduous (501 leaves sent!)but highly delicate, given the fragile state of these ancient documents.

Finally, we thank Owen Gingerich for setting aside past difficulties and sending DIOnews of our confirmation on the file’s location. Without this admirable act, the remarkablechain of recent events described here might not have occurred at all.

[Note added 1999 Oct. Thanks to current RGO Archivist Adam Perkins’ openness,Nicholas Kollerstrom was able to locate & transmit to DIO (1999/7/24) the long-hiddencentral text of Astronomer Royal Geo. Airy’s refreshingly frank & sardonic key 1846/12/8letter. (Text below at §H8.) We are grateful both to Nick and to Perkins. Though proof-certain is impossible here, DIO is obliged to point out: [1] This letter implies (& see fn 51),that (contra DIO at DA §B2) Airy never knew the actual cause (precis here at §K2) ofAdams’ publication-delay, which cost Britain the planet. (But see fn 91. And Nick’s othermajor find indicates Airy&Adams may’ve been closer in early 1846 than most historianshave previously suspected: §H6.) [2] Nothing new in the RGON file supports DIO’s 1992speculation that the prediction Adams evidently handed Airy in 1845 Oct was the same(miscomputed) one handed to Challis in 1845 Sept.4 (But the DA §G items in favor of thistheory still stand.) Regardless, see the conclusive point emphasized below at §E3.]

3This work has not only an historical benefit: Adam Perkins, the able RGO archivist, was to pickup the records to return them to England, so Elaine’s work protected Perkins (providentially, it turnedout) from suspicion of being connected to the RGON file’s gaps.[Happily, subsequent events (e.g., §H8) indicate that Perkins is as properly uncensorial as Elaine.]

4 The 1845 Sept solution (CON #32 & Sampson 1904 p.166) bears a mark of reality, time, & utilitylacking in the “1846 Oct” document, by appending current geocentric longitude. See fn 42.

Neptune File Saved, Adams Legend Lost 1999 June DIO 9.1 ‡1 5

A Celestial Mechanics’ Most Miraculous Day

A1 The 1846/9/23 discovery of the planet Neptune is the most magical predictive-mathevent in the history of the oldest science. On the morning of that date, Johann Galle ofthe Berlin Observatory received a 9/18 letter from the great Paris Observatory celestialmechanist, Urbain J. J. Leverrier, telling Galle that if he aimed his observatory’s telescopeon the ecliptic in the region of geocentric longitude 325◦.0, he would discover the eighthplanet of the Solar System (“which nobody has yet seen”, as the press was quizzicallynoting at the time: Athenæum 1846/6/13 p.612) — a jovian-gaseous giant planet whoseexistence and very position Leverrier had predicted by applying (partly in reverse) Laplacianperturbation-gravitation math, to the slight hitherto-untamably non-elliptical motion of theplanet Uranus.A2 That very evening, Galle and H. d’Arrest searched with the Berlin Observatory’sexcellent 25 cm Merz & Mahler refractor (using Carl Bremiker’s beautiful unpublishedBerlin Starchart of the region, which had been completed in 1844 but not yet mailed out,5

and thus existed only at Berlin). Within a fraction of an hour, they made the discovery— at geocentric longitude 325◦.9, less than a degree from the predicted position (§A1).On 1846/9/25 (after confirming the planet’s daily motion and nonpunctal appearance), anunderstandably dazzled Galle was able to write Leverrier (Galle’s emphasis): “the planetwhose place you have [computed] really exists.”

B British Seizures

B1 Instantly upon receipt of the news in England, a bold British claim to seize the newplanet was promoted by John Herschel, Cambridge Observatory Director James Challis,and Astronomer Royal Geo. Airy (all three University of Cambridge men) — a trio whichultimately went so overboard that they actually had the brass to push their Brit name“Oceanus” publicly for Neptune (a name which — as independent British astronomer J.Hind snickered — had the same chance abroad as “Wellington”: DA §D6). Airy was soseized by this bizarre idea that he actually wrote a (previously unknown) private letter todiscoverer Leverrier asking6 him to agree to Challis-Adams-proposed “Oceanus” — i.e., tolet the British name a French-discovered planet!7

B2 The Oceanus letter to Leverrier has got to be THE nuttiest notion of Airy’s longand illustrious career; and he naturally got back an aggrieved (though polite) Leverrierletter (10/16: fn 85) attacking John Herschel, the son of Wm. Herschel, Leverrier’s onlycompanion in giant-planet discovery. This was followed by an enraged 10/19 Leverrier letteron hunkering8 Challis’ ineptly contradictory supernationalism at home, simultaneously withdiplomacy abroad; Leverrier: “blanc en France . . . noir en Angleterre”. (DC showed that,almost a half-century after the discovery, Astronomer Royal Wm. Christie was still urgingcensorship of Leverrier’s letters, which are only now finally available unfiltered.)

5 The Berlin Observatory (whose telescope was a twin to that of Dorpat) was saving money bymailing out the high-quality Berlin Sternkarten (a project initiated in 1825 by the immortal Bessel:fn 80) only in pairs, and no other charts had come to completion in the 2 year interim (1844-1846).

6Letter in RGON file, Airy to Leverrier 1846/10/14 p.3: “If you would consent to adopt the nameOceanus instead [of Neptune], it would, I think, be better received” being more similar to Uranus. Butdid Airy ever tell Leverrier that Adams-Challis (whose claims and very names Leverrier was by thenunderstandably incensed over) had thought up this sea-faring-nation name for his planet?

7Hey, it worked in 1930 for US-discovered Pluto — which was named through H. H. Turner,another Chief Ass’t to the Astronomer Royal. Of course, this was just a diplomatic ploy — highlyagreeable to the Lowell Observatory — to merge Percival Lowell’s initials (instead of rival claimantWm. Pickering’s) into the acronym of the planet.

8See fn 82 and DA §D2.


B3 The French reacted to “Oceanus” with Paris Observatory chief Arago’s 10/5 an-nouncement of his determination henceforth to call the planet “Leverrier” instead! Havingmade this reactive choice only after “Neptune” (the name Leverrier himself had originallygiven to his planet) had already been entered into the official records of the French Bureauof Longitudes, Arago went to far as to personally (in his distinctive hand) alter that recordso that it no longer seemed to pre-empt the later decision.9 This is an instance of an honestperson believing that only by counter-dishonesty can he fend off theft.10

B4 Between the planet-deprived Brit public and the apoplectic French, Airy was undersuch intense siege that he and his family obviously feared for his job.11 His brother Wm.Airy even nightmared (§J5) over the spat. (See the ’til-now secret Airy-Adams war: §J.)B5 The all-Cantabridgian circle of §B1 alleged that the extremely talented young Cantabmathematician John Couch Adams had in 1845 made the same prediction as Leverrier, but— oops — the elements had somehow never gotten published during the year since. (Thissomehow has turned out to be some how-to-explain.) It soon came out that the CambridgeObservatory had (in secret)12 been massively searching after the planet for months (workingtowards an ultimate triple-sweep of 300 square degrees of sky!),13 partly on Adams’ private— again, unpublished — instructions (§E), with Director Challis working nightly (headinga three-man team)14 at the eyepiece of the Observatory’s 30 cm telescope (largest refractorin England, established in 1835 through the influence of John Herschel and Airy — see§I1), according to a plan allegedly discussed (again, entirely in private) at an 1846/6/29RGO board meeting in which Airy, Challis, & Herschel participated. (Nothing of this wasentered into the official minutes of the meeting.)B6 DIO has taken the hotly Brit-resented position that Adams should not be recog-nized as co-discoverer because of the secrecy he (and his Cambridge circle) deliberately

9Bureau des Longitudes, Compte-rendu 1846/9/30 p.3. The alteration made it seem as if “Neptune”was merely discussed that day as a possibility. A photograph of this document was sent to DR by theBureau des Longitudes on 1967/9/26.

10 Deceit (e.g., §I1) frequently produces a reflection. It’s rather as if dishonesty meets one of the testsof life: reproduction. For a case similar to Arago’s, see DIO 4.3 ‡12 fn 4. (See also below: ‡3 §F7.)

11At age 13, Airy had seen his father lose his job. Rob Smith has made the sort of observation whichepitomizes historians’ superiority to scientists in some areas: alot of commentators have found it hardto believe that lordly Geo. Airy would be as frightened as he was over the Neptune fracas. But Robjust made a deft perspective-shift-observation and commented: Airy had not yet achieved his uniquestatus (by which we see him today) as the greatest of all Astronomers Royal.

12Hind knew of Challis’ search by mid-Sept (CON #10), but not its double-prediction cause.13Myles Standish asks one of those common-sense questions that can get overlooked by scholars who

get too bogged down in details: the Brits were alone in the secret that 2 math analyses were pointingto the same part of the sky, so why was the Brit search so tediously wide while the Berlin search wasso efficiently narrow? (The answer is key: Adams was pointing to various parts of the sky.)

14Challis, a Mr. Morgan, & RGO’s off-the-books loaner James Breen. The official pre-DIO recordhad Challis refusing RGO help. See Smart 1947 p.27 and M16:403 (Airy) & 404 (Challis) vs DA§B1. It is a famous part of the British Neptune tragedy that Challis in 1846 Aug accidentally stoppedcomparing stars (in two lists of the same slice of sky) after 39 stars when the 49th “star” was Neptune.What has not up to now been asked is: why was Breen not doing this work, promptly, for all stars?Challis’ previously unpublished 1846/8/7 letter to RGO begs for the help of Breen (an able computer)in the search, so: why didn’t Breen (upon his mid-August arrival at Cambridge) compare every startaken so far? Partial answer: one of the double-lists containing Neptune was a small thing, with justa few relatively bright reference stars — and Challis wasn’t expecting an object nearly as bright asNeptune proved to be. (A deep planet’s dimness is about proportional to the distance’s fourth power.)But the other star-list with Neptune on it was full, so Breen should’ve been rapidly comparing it &all other data right away. Question (suggested by Challis’ hogging the eyepiece, too): was Challislowering the efficiency of the search in order to make sure that he made this discovery himself, bothoptically and cartographically? (But note the implicit integrity, too: alot of project-chiefs would letothers do the work and then grab the credit anyway. See, e.g., DIO 4.1 ‡2 fn 39.)


maintained throughout. Among other considerations: acceptance of a nationalistically15

inspired post-discovery claim-jump would set an intolerable precedent,16 converting theissue of credit for research-advances into merely a question of who has the most politicalpower. (Too often the case anyway.)B7 Adams was said to have deposited with Challis (1845 Sept) & Airy (1845 Oct) the or-bital elements for an unknown planet, the contended Adams result known as “Hypothesis 1”(which we will abbreviate as just “Hyp 1”) — a planet of mean distance 38 AstronomicalUnits from the Sun (over 1/4 too large) and in the eastern part of the constellation Capricorn(about where Neptune really was). The whole Brit case for priority is falsely (fn 20) hungon this single document. Problems with the Hyp 1 legend: [a] Neither 1845 document wasdated by Adams (hardly the behavior of someone who believes he’s lodging an immortalprediction!) — and no cover-letter addressed to either party has ever been produced; thus,both documents were dated (year & month, without precise day) only later, and in therecipient’s hand (DA §§C7-C8). [b] All continuous records of these late-1845 to mid-1846events — Adams’ diary,17 Herschel’s diary (photocopies sent DR by J.Moll, C.Henderson,C.Cordova, U.Texas Austin), Airy’s diary, Challis’ diary, RGO minutes (§D4 item [b]),RGO visitor’s book — are either blank (on Neptune) or missing (DA §I9). [c] The solutiongiven Challis in 1845 Sept was not Hyp 1 (fnn 48&62 and DA §§F1-F2; and see fn 4).[d] At the time of discovery (1846/9/23), Adams was in fact pointing Challis over 10◦ tothe west of Neptune’s actual position. (See below at §G; details at DA §E8.)B8 British excuses for Adams’ nonpublication & non-reply to Airy’s nice 1845/9/29& 1845/11/5 notes of reception of Adams have been as varied as ridiculous-cover alibisalways are: Adams didn’t like to write letters18 (but he and Airy were both at the 1846/2/13Royal Astronomical Society meeting, so Adams could have spoken to Airy then, or 1845Dec or 1846/7/2: see fn 68 & §B11 [also §H6]); he was shy (though not too shy to helppublicly promote the Cantab name for the planet, “Oceanus”, after the discovery: fn 82 &DA §D6); he procrastinated (Challis to Airy 1846/12/19); he was a naıve simpleton (§H12);he (by bad-luck) accidentally missed seeing Airy at the Royal Greenwich Observatory in1845 Sept (DA §F1); he was (fn 89) disappointed at not talking with Airy — a whollymythical “snubbing” — when he returned in 1845 Oct (see Airy’s irate reaction to this“rank fib”: §J8); Adams just-missed (yet another oops) an 1846 Sept BAAS meeting19 atwhich (he later stated) he was planning to announce his results (yet, in fact, even weeksafter the discovery Adams was reluctant to produce his numbers: see §H11 below).B9 Every one of these alibis was easily exploded in DA (e.g., §D1). But such amusingexercises in apologia should not divert scholars from the true, crucial, and exceedinglyelementary cause of Adams’ nonpublication (which he himself wrote out, in a little-notedpassage: DA fn 5) — he had simply not completed his math:20 the central reality of

15See DA §§A8&D8. Brit fervor for Adams was particularly unseemly in a toppe nation. (Similarto, e.g., current US madness to be first in every sport at every Olympics. When one is the richestnation on Earth, some modesty ought to be in order; however, the process of getting to the top in thefirst place evidently leaves a residue of pushiness that continues long after its need has passed.) HadAdams been, say, Bulgarian (i.e., without the power of Britain behind him), one doubts that anyone inBritain or elsewhere would have paid much mind to his peculiarly late claims.

16See Biot’s common sense at DA §I11.17 [Kollerstrom, with St.Johns archivist Jonathan Harrison’s help, has just found a 1846 March piece

of Adams’ diaries (JCASJ 20/22/3); but it has nothing on the search for Neptune. See §H6 & fn 73.Adams left dated memos (e.g., fn 81) which could be selected excerpts from now-missing diaries.]

18See Adams to Airy 1846/11/18 p.4 (RGON).19BAAS Pres. J. Herschel recollected (DA §D2) he’d mentioned (9/10) the planet prediction at the

BAAS meeting; but (oops cubed) he didn’t cite Adams. Adams thought (M16:408) of giving a paper butinstead “stayed up late” calculating 9/10 (JCASJ 20/21/4). Oops4. Challis skipped his own scheduledpaper (Athenæum 1846 p.963). Oops5.

20 See §H5 and DA §I7. (Also Airy’s too-late lament at M16:414.) Adams-defenders point out theresemblance of Adams’ alleged 1845 Autumn predicted longitude to Neptune’s — without recognizing:


the Cambridge failure to net Neptune, which so unambiguously shoots down the wholeclaim (of British priority) that no Brit mythmaker is willing to face it. (In answer to thenatural question of why Cambridge didn’t discover the planet in 1845, Challis [SP p.li, hisemph] doubted not “the evidence . . . of the existence of the planet, . . . [however] itsposition was determined but roughly, [thus] . . . a search for it must necessarily be long andlaborious. . . . consequently I had no thought of commencing the search in 1845, the planetbeing considerably past opposition at the time21 Mr Adams completed his calculations.”)B10 Most historians have bought at least partly into the mythology of non-publishingAdams as prior co-discoverer, a legend that can only be maintained by blaming Challis andAiry for discouraging hero Adams through lack of understanding and initiative. (None ofwhich explains why Adams himself didn’t publish or announce; after all, he delivered apaper at the Royal Astronomical Society in 1846 April, but on an entirely different subjectthan Uranus & Neptune.) This has left utterly illogical gaps in the history. (Gaps we nowlearn Challis explicitly stated 1846/12/19 to be a good idea: see below at §H.)B11 Nor has the secrecy of Airy and Challis ever been creditably explained. (Obviousactual explanation: Airy hoped22 to bag Neptune with the telescope he got for Cambridge(§B5), using the Cambridge-only secret23 that two math-astronomers had pointed to nearly

Adams knew (and explicitly stated: DA fn 5) that since all his 1845 work was based on an assumed meandistance for the disturbing planet, he had no “satisfactory” solution until 1846/9/2. (His Hyp 1 meandistance was 38 AU, very different from his final value and from the truth — though, in extenuation, seeRawlins 1970G.) I.e., he believed he couldn’t reliably predict Neptune’s longitude until he had repeatedthe work with a different mean distance (diminished by about 3%) in order to discern two crucial trends:[i] Did this alteration improve or degrade residuals’ rms? [ii] What would be the alteration to the all-important longitude? — THE answer which telescope-searcher Challis had to receive. But Adams didnot conclude work on this until 1846/9/2 — when he got it quite wrong. (Letter to RGO: see §G1.The result, which DA called “Hyp X”, was over 10◦ off.) This was sent to RGO right after Leverrierhad published his analogous distance-variation-based solution (1846/8/31), the longitude for whichwas correct to within one degree. Apologists’ obsession to promote Adams’ proximate 1845 Autumnsolutions (as some kind of priority) ignores not only Adams’ own nonexcitement (§B7) at this latterly-aggrandized moment (he didn’t even note the event in his diary: §D3) but also the little-considered factthat Adams had been developing lots of solutions (both before and after the 1845 Autumn ones), hugelyswinging 35 degrees in longitude, from about 315◦ up to about 350◦. If we only count the solutionshe actually handed to Challis & Airy, the range is still over 20◦: from 315◦ (Hyp X, 1846/9/2) up toabout 336◦ (Hyp W, 1846/7/20). Thus, Adams’ lodged predictions covered a range more than 20 timeslarger than Leverrier’s under-1◦ error in Neptune’s predicted longitude. (See DA §F3 and its Table 1.)True, Leverrier’s final 1846/8/31 limits had a range of 14◦: longitude 321◦ to 335◦, Leverrier 1845-6p.436. But this bracket resulted from testing a coherent theory, so it is not comparable to Adams’ yearsof diffuse and somewhat disjointed solutions, each of which had its own unstated imprecision. I.e., ifwe wish to include solutions’ formal errors, this will inflate Adams’ already-huge uncertainty-rangeby ordmag ten more degrees. Analogously, after the 1930 discovery of Pluto, Wm. Pickering also(for post-discovery-promotion) rather shamelessly selected the in-hindsight-better-looking among hisyears of various disparate predictions of trans-Neptunian planets. Since he even mingled pieces ofincompatible solutions, Pickering’s post-discovery self-advertisement was less creditable than Adams’;but, at least his predicted data were published before planet-discovery.

21 An undated Adams memo (JCASJ 20/23/2) similarly explains his not answering Airy’s 1845/11/5letter. [Extant 1845 Autumn Adams outdoor star observations (JCASJ 20/22/1) are nowhere nearNeptune.] Yet Galle found Neptune roughly the same time of year. But, unlike the 1845 Adams,Leverrier had a precise conclusion. [See also fn 74 & fn 94.]

22Perhaps not only for glory but to atone for his failure to push Adams’ math along earlier on.23 An oddity about Adams’ silence that bothers DR & Standish: yes, one can explain his nonpub-

lication as due to his unsurety. But: wasn’t it also awfully convenient for Cambridge? His stayingquiet gave a terrific probabilistic advantage to Cambridge in the planet-search. Was Adams asked (byChallis? fn 67) to stay quiet about Hyp 1, with reward promised for cooperation? Tempting theory;but, it alone can’t explain the §E2 evidence against Adams having had confidence in Hyp 1, assumingit even existed yet: §D4 item [a]. And, if he had a firm solution but kept it back to help Cambridgecapture the planet, then why be so slow to commit to any numbers even after the discovery: §H11?


the same spot in the sky. See DA §B5.) Upon publication of Leverrier’s first roughprediction-estimate of Neptune’s place (1846/6/1), Airy wrote him (6/26), but didn’t men-tion Adams’ name! At the time (1846 July) Airy was launching his vast secret sky-searchfor Neptune, the leading theoretical celestial mechanist of the world (P. Hansen) lived for3 weeks in Airy’s home: no mention was made of Adams. When Airy & Hansen were outwalking and accidentally bumped into Adams at Cambridge 1846/7/2, Adams said nothingof his work, even though equations of Hansen (explicitly identified by Hansen’s name, inAdams’ hand) are right in Adams’ Neptune mss. (See DA §B6.) Nor did Airy speak up(on 7/2, or at any other time during Hansen’s 3 week stay at Airy’s home: DA §B6), thoughjust 3 days previously, Airy had told the RGO board (§B5) that Adams’ work co-justified avast search by the biggest telescope in England! (Tell me nobody was conspiring here.)B12 But, even before consulting original documents, DR in the 1960s had already seenenough oddities in the traditional saga that when he wrote RGO asking to see the Neptunepapers, he felt obliged to express honestly his (non-adamant) skepticism. (See DB §D6.)B13 Though David Dewhirst of Cambridge openly sent the whole (extremely revealing)Cambridge Observatory Neptune file (CON) in 1967 (DB §D), the RGO’s reaction wassinuous and cagey. (E.g., in RGO’s correspondence with DR, letters on Neptune were onprivate stationery, while all other letters were on official RGO stationery: DB §H1.) Detailsbelow at §C3 & fn 29. The eventual upshot: the RGON file was never forthcoming. DRhad (1966-1972) spent a large amount of labor in research, math,24 and writing (ordmag100 pages) towards a book on the Neptune case, a project that ultimately atrophied while hewaited patiently and naıvely through two years of RGO sham.25 (So a high RGO official’shiding of documents stole not only the Neptune papers for many years — but also destroyeda book permanently. Not trifling misdeeds.) Ultimately, RGO in 1969 said the file was lost— without mentioning what DR only began hearing later, namely, that it had been stolen.Later yet, DR learned that the “thief” was extremely close to the Astronomer Royal.B14 In DA & DB, DIO revealed this person’s name & high RGO position and publishedour (unreplied-to) letters requesting his assistance with the RGON file.

C The RGO Neptune File’s Startling ReappearanceC1 In the early part of 1999, DIO received word that the stolen Royal GreenwichObservatory RGON file on the 1846 discovery of Neptune had been recovered. Despiteseveral knowledgeable parties’ reluctance to discuss the matter, it became clear that: thevery person fingered (§§B13-B14) by DIO as having taken the file had died in Chile — andthe file had been found in his home.C2 As noted (§B14) by DIO, this person had been (roughly when the RGON filedisappeared: in the 1960s) the Chief Assistant to (and top confidante of) then-AstronomerRoyal Richard Woolley — the very party DR had asked (in 1967-1969) for permission tosee the file. (We note that — over more than a century of time — no less than FOUR26

Astronomers Royal have been associated with suppressions27 of material in this file. But

24Some appears in Rawlins 1970G and DA.25It was sham by even the present RGO archivist’s least-discreditable version of events: §C5.26 Geo. Airy in 1846 (DA §B2 and below), Wm. Christie in 1893 (DC §§A3-A4), Harold Spencer

Jones in 1946-1947 (DA fn 34), and R. Woolley in the 1960s (see §C3 and DB). Note: both RGOarchivists Philip Laurie and Janet Dudley correctly identified (privately) who had stolen the file: DB§B6. Are we to assume that they knew — but that the thief’s closest confidante Woolley didn’t knowand (assuming Woolley genuinely wanted scholars to see the stolen material) wasn’t able to contact hisown chief subordinate and order him to: put the file back PDQ? Note that Woolley’s having deputedhis Chief Ass’t to get into the RGON file was indicated by the latter’s testimony in 1996: see §C7item 4. Compare to DB §I1.

27Despite over a century of high-level efforts (fn 26) to hide or censor the RGON file, most Britofficials close to this case echoed (at least until 1998) the RGO 1967 line that there is nothing-new in


in fairness, we should repeat our DC §A8 note that virtually all British astronomers areinnocent of any kind of censorship in connection with the Neptune case.)28

C3 Throughout an extended 1967-1969 correspondence, RGO gave out a series ofconflicting stories: at first, RGO said it couldn’t find the file, then said it was making a listof “letters for examination” (but the lister was ill: fn 29), finally after two years of delaysreverting to again claiming it couldn’t find the file. (Full phantasmagoric exchange printedin DB. Central oddity stressed here at §C5.)C4 On 1999/4/14, DR told the current RGO archivist, Adam Perkins (University ofCambridge Library), that it looked like the RGON file had disappeared just about the timeknown-skeptic DR had asked to see it. Perkins replied that it was believed that the file haddisappeared in the early 1960s instead. I pointed out this timetable’s contradiction of whatP. Laurie, Perkins’ own predecessor at RGO, had told DR (in detail) in 1967.29 Perkins saidthat, well, Laurie was not being entirely truthful.C5 DR’s reaction: if the only way the RGO archives can deny a contra-DR coverup (i.e.,deny that it indeed possessed the RGON file even while keeping it from skeptical DR) is byindicating that it was itself not being honest in 1967, then: may DR perhaps be excused fornot taking the RGO’s entire performance30 quite at face value?C6 Analogously, the former Chief Ass’t to the Astronomer Royal, who was hiding thewhole hefty RGON file in Chile — about 500 pages! — along with some other filchedRGO archival material, was in 1993 asked31 by DIO for photocopies of the file. His refusalto reply was duly published32 (“Chile Nonreception”) in DB §H.C7 DIO’s two letters to Chile went cc to Ian Ridpath and Charles Kowal. Ridpathfollowed up and got an e-mail reply from the former Chief Ass’t, which Ridpath relayed toDIO on 1996/8/26. Since the standard Brit alibi (for the 3-decade hiding of the RGON file)will undoubtedly be of the lone-crazed-Chief-Ass’t stripe, we will here quote extensivelyfrom the message to Ridpath. Note especially several indicators of the writer’s detailedmemory — as well as (item 4) his Neptune-involvement’s instigation33 by RGO:

All I can recall . . . . about the historical files at Herstmonceux [RGO]:1. They were moved from Greenwich and spread out in several locations

at the Castle [Herstmonceux] . . . .

the RGON material. (See fn 29. And DB §D4.) They also affect total neutrality in the matter, which Ilearned through another source was purely thespian. (See DIO 2.1 ‡1 §M4.) I was told that the verymention of DR in certain British presences chills the air.

28However, it is also unfortunately true that England has not shown much interest in publicizing theAdams legend’s manifold peculiarities. E.g., our thanks to the British Astronomical Assoc (DC §A6)were premature: it turns out that the heretical speech there cited was never mentioned in literature sentto BAA members. (BAA guru Patrick Moore cannot abide unorthodoxy in this matter; of course thatlamentable circumstance has nothing to do with serious British astronomy.).

29 See §C3. DB §§E10-E12 (RGO archivist P. Laurie to DR 1967/9/8): “Just after I wrote you atthe end of May, Mr. Rickett, who was dealing with the manuscripts, suffered a stroke from which hehas not yet recovered. He had drawn up a list of letters for examination although these, I fear, do notappear to contain any new material. I shall try to give these my undivided attention in the near futureand send you notes on their contents.”

30Mobian-merry-go-round summarized at §C3 and DB §§H1&I1.31DB §H13.32Since others were too timid to publish his name in the file-theft connection while he was alive and

powerful, DIO did so both in DA & DB. Now that he is dead, we can safely leave to the very samefolks explicit perpetuation of his infamy in this connection.

33Friends of the former Chief Ass’t are downhearted that happy memories of his considerable positivecharacteristics (and kindnesses to colleagues) are being besmirched by revelations that he hid the RGONfile for a third of a century. In amelioration of this seriously contra-academic deed it should be stated:DIO has argued (§L, §C7 item 4, DA §C5, & DB §I) that he did not do so on his own authority.(Ironically, the theft may have had an eventual helpful upshot: NOAO’s openness might not have beenfully matched had the papers turned up in England under traditional auspices.)


2. Some were in the attic . . . . spread out in piles . . . . The roof leaked. . . . I remember one particular pile because a few letters on top pertainedto British reception of Einstein’s theories and there was a suggestion that theopposition to Eddington’s nomination of Einstein for the Gold Medal of theSociety was motivated by other than scientific considerations.

3. No one was officially in charge of these files but the solar observer,Phillip [sic] Laurie, had a personal interest. . . . Eric Forbes . . . worked withLaurie.

4. As Chief Assistant to the Astronomer Royal, I was requested to preparebiographical and historical material from time to time. These involved abiography of Airy and other British astronomers. Laurie supplied me withdata from files for these. I recall his showing me a manuscript that hadobviously been incorrectly included in the Maskelyn [sic] file, that proved tobe one of the earliest attempts to solve the orbital elements of an eclipsingbinary. This was later published in the Observatory magazine.

5. My own contributions to the files were (a) some miscellaneous materialsupplied to me in correspondence with Airy’s granddaughter and (b) myinterest in the relations between Newton and Molyneux which were held inthe Portsmouth Public Record Office and transcripts of which I gave to Laurie.

6. The direct answer to your question34 concerning the Neptune papers —my knowledge of this matter is based on notes35 given me by Laurie for (a) areview of a book36 on the subject by M. Grossner (?) and (b) a biography ofAiry.

7. Certainly Laurie, if he is still alive,37 can help you infinitely more thanI can.

C8 The former Chief Ass’t’s very coherent38 denial that he had the RGON file satisfiedsome. But DC regarded the reply as suspicious, since no response (not even to top Britofficialdom: DC §§A7-A8) had been forthcoming while Laurie lived. So DIO proposedto 2 different Brits that the next request to Chile should be for: a copy of the purportedLaurie notes. (Suggestion published at DC §A7.) That is where the case was left untilit was proved directly (by post-death search of the denier’s home) that the foregoing wasa bluff: texts of the inquiries he was ducking, as well as his denial that he possessed theRGON file, were evidently found along with the file. We now turn to the hitherto unknownor unconfirmed material in the RGON file itself, the most important parts of which relateto the credibility of the standard excuses (§B8) for Adams’ crucial post-1845/11/5 silence.

D Key Adams Document #1: Memo RD1 One of the two long-lost physical bases of Britain’s priority-claim has been recoveredin the RGON file. (How it ended up in Chile is a tale that will surely be re-told as longas there are astronomers in our Solar System.) This famous document has been called

34Note by DR. The question (published in DB §I1 item [f]) which he was answering was: how couldthe former Chief Ass’t have — in a 1971 article — cited letters only available in a file that had (DB§G3) disappeared in the 1960s?

35[Note by DR: Catch the resemblance to Laurie’s 1967 words (fn 29) — which the former ChiefAss’t had recently received via DIO (DB §E12; 1994).]

36The book was Discovery of Neptune by Morton Grosser (Harvard 1962). The review (probably themost perceptive anyone produced, as noted at DA §E7 & DB §H8) was published the following yearby Sky&Tel (1963/4).

37Ridpath notes that Laurie died in 1983.38As Ridpath remarked at the time.


“Memo R” for convenience throughout DIO’s analyses. Memo R contains the orbitalelements of Adams’ Hyp 1 (§B7), which is the core of the whole Adams controversy.D2 DA §C7 was first to point out the oddity39 that the only date on Memo R is in Airy’shand, not Adams’. (No cover letter survives for Memo R, nor has Adams’ card survived:§D4.) The 1845 Oct date now on the document has to have been added later, since on thedate40 he received Memo R, Airy must have known what day it was.D3 Which puts him one up on Adams, who didn’t! Even though Adams was (unlikeAiry) absolutely certain to have been in physical contact with Memo R on the very dayof the sacred event of its Deposit at RGO, nonetheless, his newly available 1846/10/15letter to Airy can only guess (p.2) that it was “about”41 1845/10/20. Upon our carefulconsideration, this statement tells us a good deal: [a] This allegedly-epochal event wasnot entered in Adams’ 1845 diary (now conveniently missing: DA §I9) — or indeed intoany other continuous record of events. [b] Clearly he reasoned out a rough date fromhis other dated documents at hand (e.g., the dates of his post-vacation travel from hometo Cambridge). What does it tell us about the import (to Adams himself, at the time) ofthe deposit of The Historical Document (1845 Oct unknown-planet elements, purportedlyMemo R, containing Hyp 1) that: Adams wrote down the date of his vacation-end butnot of his grand document-deposit? — which he later pretended was meant as a kind of“publication”.42

D4 We conclude this section with two further items in connection with the date of Airy’sreceipt of Hyp 1: [a] The Hyp 1 math mss (JCASJ W.16 §E IV-E V) leading to it comprisethe sole mature Adams perturbational solution on which there are no dates (DA §H1) —except, that is, for a portion which is dated 1845/12/16 (DA §G3) some months after thesolution is supposed to have been handed to Airy. (See fn 20.) [b] The Airy home’s wispyattestation to 1845 Oct receipt of the immortal Memo R is found in a hitherto-hidden RGONletter, Airy to Adam Sedgwick, 1846/12/8 p.1 (emph added):

I have no doubt that the facts of Adams’ [alleged 1845 Oct] call were asyou and Adams have made out. My wife seems to have a notion of his card43

being brought to her in my absence, but nothing further is known. [DR: See§B7 item [b].] I was at the end of October 1845 busy almost every day at theGauge Commission,44 and on October 29 my boy Osmund was born. — I amashamed to mention these things. . . .

With such squishy, gappy testimony in witness to the glorious (if undated: §D3) impartingof Adams’ 1845 Oct solution, well — little wonder the full RGON file has never previouslybeen seen by anyone but Cantabs and Astronomers Royal.

39For further time-line problems, see ibid §G3 & fn 65.40Generally understood to have been a bit later than the date of Deposit. Airy was uniquely notorious

(see DA fn 36) for writing dates on anything that came near him.41Adams originally said (RGON 1846/10/15 to Airy p.2) “about the 20th of October 1845”. A later

Adams memo (newly-found in JCASJ: fn 21) makes it Oct 10 (which, if true, relates to DA §G1). Inany case, Adams’ recollection of this central date is revealingly infirm. Smart 1947 p.19 computesOct 21 from an Oct 23 Adams letter (JCASJ 16/2/3), describing the Great Day as simply: “Tuesday”.

42 See §K1 & fn 93. The ungrandiose actual purpose of Adams’ 1845 Autumn trips to RGO is inducedat DA fn 48. (Note: RGO’s optical ability to search for Neptune was far less than Cambridge’s. Seealso here at fnn 4, 69, & 74.) If one takes seriously Adams’ claim that he was thereby attemptingto register (WITHOUT DATE) his discovery for posterity, one is eventually reduced to pleading theclient as temporarily inane (Sedgwick to Airy 12/6 p.2, emph added): “Adams tho’ a great philosopherin his way [DR: i.e., when Brit-claim-mythology wants him to be brilliant (which he was)], has shownno worldly wisdom — and has acted like a bashful boy rather than like a man who had made a greatdiscovery.” See also §H12.

43Note by DR: Adams gave card & message (fn 89) and “a note for” Airy (JCASJ 16/2/3), vs §D2.44[Nick Kollerstrom (1999/7/24): “I think it’s a shame your DIO articles never mention the driving

passion in Airy’s life, viz. railway trains.”]


E Key Adams Document #2: Memo WE1 Besides Memo R, the other vital document traditionally brought forth to support theBrit claim on Neptune is an 1846 July document — called “Memo W” by DA — whichAdams computed for Challis, to tell him where the Cambridge Observatory telescope shouldbe aimed, to find Neptune. (The full data of the bottom half of Memo W are publishedfor the first time here on p.14: Table 1.) Smart 1947 (p.31) is typical of pro-Adamshistories in quoting Challis’ argument for Adams, based on Challis’ having seen Neptuneon 1846/8/4&12 “entirely [due to] my having, on those days, directed my telescope towardsthe planet’s theoretical place, according to instructions given me in a paper Mr. Adams hadthe kindness to draw up for me.”45 The cited document is Memo W.E2 However, after analysing Memo W (THE key document46 revealing the truth behindAdams’ nonconfidence and the attendant British confusion on Neptune’s place), DR wasamazed to find (DA §B4) that it is not based upon Hyp 1 as Challis had certainly implied(§E1) and therefore all pre-DIO historians had always quite naturally assumed. (Challishad said at M16:421 that Memo W was “entirely from theoretical data”, but he coyly hadn’tsaid whose theoretical data: fn 47.) According to the up-to-now-accepted history, Hyp 1was Adams’ theory at this time. But Memo W is instead based on a simple 38 AU circularorbit (which Adams had indeed once used, but long before his now-famous elliptical Hyp 1).This document’s circular calculational basis was induced in DA fn 21, and a full circular-orbit check is provided here in Table 1. (DA fn 19 also notes that this computed ephemeris’central time epoch is based on the Wartmann object we will briefly take up here in §F3,which Challis denied Adams used: §F4.) And all its elements and limits are basically47

those of Leverrier’s very recent 1846/6/1 publication. Further: Adams in Memo W statedthat his math-derived planet is at 325◦ “very nearly”. But DIO has earlier pointed out(DA §G9) that, for Adams’ chosen 1846/10/6 math-epoch, this is the longitude not of thelegendary Hyp 1 (329◦) but of later-Memory-Holed math-mistake-based48 Hyp G (325◦).E3 Thus, either Hyp 1 did not yet exist, or Adams had no confidence in it. But the pointis that either interpretation is lethal to the Adams Hyp 1-priority myth.E4 In Table 1, we compare Adams’ figures (A) to orbits generated by DIO from ellipticalHyp 1 (H) and from a circular orbit (C). (Both the H and the C orbits have Bodean meandistance: 38.4 AU; θ = true longitude at 1846/8/29 Greenwich Mean Noon.) One doesn’teven need statistics to see that the circular orbit (C) fits far better49 — an unevadableconfirmation of DIO’s theory that Adams’ (supposedly 1845) Hyp 1 was not his actualbelief even as late as mid-1846. Note that in Table 1, the disagreement (of Hyp 1) withthe ephemeris grows greater the farther one gets from opposition, mostly because ellipticalHyp 1’s heliocentric distance in 1846 was only 32 AU, not 38 AU; so, the parallactic effectbecomes increasingly pronounced the greater the time before or after opposition.E5 Since Adams’ allegedly-1845 Memo R was the result of long & famous effort(detailed in Sampson 1904 and Smart 1947) at going beyond a circular-orbit to find anellipse (Hyp 1) which fit the Uranus data much better, it is peculiar & suspicious that (itturns out): as late as mid-1846, Adams still had confidence only in a circular orbit.(Recall DA §C1: Challis’ 1st public claim for Adams put Hyp 1 not before mid-1846.)

45SP p.liii or p.6 of the original published report (copy in RGON), 1846/12/12..46Memo W was transmitted by xerox to DR by Cantab David Dewhirst, 3 decades ago.47 Leverrier 1845-6 (p.917): heliocentric longtude 325◦±10◦ (epoch 1847/1/1). A copy of this

statement survives in Challis’ hand, partly in French (CON #34, therefore adjacent to Memo W, whichis CON #35[a]). The only distinction between Memo W’s and Leverrier’s elements & limits is epoch(Adams’ was 1846/8/29): a trifling 1◦/2 constant mean-longitude difference.

48 See DA §F2. Hyp G (DA §G) was handed Challis in 1845 Sept. Not published by the principals.49 The circular orbit residuals (C) are smaller than the Hyp 1 residuals (H) by factors of 2 in decl &

3 in R.A. (A slightly smaller radius can improve C’s fit to Memo W; roughness perhaps from misuseof 2nd-order arithmetic scheme in computing Memo W: DA fn 21.) No member of the 25 decl data inthe C columns (of Table 1) deviates from the corresponding A column datum by more than 1′.


Table 1: Checking Adams’ 1846 July 20 Ephemeris (Bottom Half Memo W): Hypothesis 1vs Circular Orbit

For θ = 315◦

Date αA δA αH δH αC δC

Jul 20 21h11m.1 -16 ˚ 16′ 21h11m.2 -16 ˚ 15′ 21h11m.1 -16 ˚ 16′

Aug 9 21h 9m.1 -16 ˚ 24′ 21h 9m.2 -16 ˚ 24′ 21h 9m.4 -16 ˚ 23′

Aug 29 21h 7m.5 -16 ˚ 31′ 21h 7m.3 -16 ˚ 32′ 21h 7m.7 -16 ˚ 31′

Sep 18 21h 6m.2 -16 ˚ 37′ 21h 5m.7 -16 ˚ 39′ 21h 6m.3 -16 ˚ 37′

Oct 8 21h 5m.1 -16 ˚ 42′ 21h 4m.6 -16 ˚ 44′ 21h 5m.3 -16 ˚ 41′

For θ = 320◦


Jul 20 21h31m.3 -14 ˚ 41′ 21h31m.5 -14 ˚ 41′ 21h31m.3 -14 ˚ 41′

Aug 9 21h29m.5 -14 ˚ 49′ 21h29m.6 -14 ˚ 50′ 21h29m.7 -14 ˚ 49′

Aug 29 21h27m.9 -14 ˚ 57′ 21h27m.7 -14 ˚ 59′ 21h28m.0 -14 ˚ 57′

Sep 18 21h26m.5 -15 ˚ 4′ 21h26m.0 -15 ˚ 7′ 21h26m.5 -15 ˚ 5′

Oct 8 21h25m.3 -15 ˚ 10′ 21h24m.8 -15 ˚ 13′ 21h25m.5 -15 ˚ 10′

For θ = 325◦


Jul 20 21h51m.3 -13 ˚ 0′ 21h51m.5 -12 ˚ 59′ 21h51m.3 -13 ˚ 1′

Aug 9 21h49m.5 -13 ˚ 9′ 21h49m.7 -13 ˚ 9′ 21h49m.7 -13 ˚ 9′

Aug 29 21h47m.9 -13 ˚ 18′ 21h47m.8 -13 ˚ 19′ 21h48m.0 -13 ˚ 18′

Sep 18 21h46m.5 -13 ˚ 26′ 21h46m.0 -13 ˚ 28′ 21h46m.5 -13 ˚ 26′

Oct 8 21h45m.1 -13 ˚ 33′ 21h44m.7 -13 ˚ 35′ 21h45m.3 -13 ˚ 32′

For θ = 330◦


Jul 20 22h11m.0 -11 ˚ 14′ 22h11m.3 -11 ˚ 13′ 22h10m.9 -11 ˚ 15′

Aug 9 22h 9m.3 -11 ˚ 24′ 22h 9m.6 -11 ˚ 22′ 22h 9m.4 -11 ˚ 23′

Aug 29 22h 7m.7 -11 ˚ 33′ 22h 7m.7 -11 ˚ 33′ 22h 7m.8 -11 ˚ 32′

Sep 18 22h 6m.2 -11 ˚ 41′ 22h 5m.9 -11 ˚ 43′ 22h 6m.2 -11 ˚ 41′

Oct 8 22h 4m.7 -11 ˚ 49′ 22h 4m.4 -11 ˚ 51′ 22h 4m.9 -11 ˚ 48′

For θ = 335◦


Jul 20 22h30m.4 -9 ˚ 23′ 22h30m.7 -9 ˚ 22′ 22h30m.3 -9 ˚ 24′

Aug 9 22h28m.8 -9 ˚ 33′ 22h29m.1 -9 ˚ 31′ 22h28m.9 -9 ˚ 32′

Aug 29 22h27m.2 -9 ˚ 42′ 22h27m.3 -9 ˚ 42′ 22h27m.3 -9 ˚ 42′

Sep 18 22h25m.7 -9 ˚ 51′ 22h25m.4 -9 ˚ 52′ 22h25m.7 -9 ˚ 51′

Oct 8 22h24m.1 -10 ˚ 0′ 22h23m.9 -10 ˚ 1′ 22h24m.3 -9 ˚ 59′

Variables: θ = true heliocentric longitude 1846/8/29 (opposition-date of Adams’Wartmann-based planet); α = geocentric right ascension, δ = geocentric declination.Subscripts: A = Adams’ ephemeris (Memo W); H = Hyp 1; C = circular orbit.The only portion of this ephemeris hitherto published (M16:421) is that for θ = 325◦.See fn 49 for comparison of residuals’ rms (H vs C).(Note: The fit of Adams’ 1845 Sept solution is also inferior to the circular orbit, thoughvery slightly better than that of Hyp 1.)


F Challis Sinks Deeper into Memo WF1 So, in brief, we have just found that Brit Key Document #1 (§D) is contradictedby Brit Key Document #2 (§E)! In fact, the situation is worse than contradictory — it isanachronistic. (Recall that §D4 item [a] also finds Adamsian time flowing backwards.) Butwe have still not exhausted the catalog of Brit headaches about Memo W.F2 First, Challis published (M16:421) only the part of the ephemeris for a 325◦ planet— omitting50 the adjacent ephemerides for 315◦, 320◦, 330◦, and 335◦. (In Table 1, wecheck the whole ephemeris to show that a primitive circular Bodean orbit fits it much betterthan Hyp 1 for all five cases Adams tabulated.) Second, there’s the little matter that: allthis is at the bottom half of the document.F3 Every one of Challis’ public reports — even while (§E1) publicly founding Britain’sNeptune claim upon the bottom half of Memo W — omitted to mention51 the entire TOPhalf, where resided an Adams orbit (also circular) based partly upon a then-unaccounted-for object sighted in 1831 by Swiss astronomer Louis Wartmann.52 This version (called“Hypothesis W” in DA) of Adams’ remarkably hyperactive planet was at longitude 336◦,over 20◦ to the east of the solution he issued just 6 weeks later (§G1), which DA called“Hypothesis X” (315◦ longitude). One can readily understand why Challis was gettingincreasingly confused53 about where to point his telescope!F4 Not only was (as DA §B4 noted) this erroneous Hyp W orbit never mentionedanywhere (until DA, that is), but: we now find (from the newly recovered RGON file)that Challis was stating54 to Airy (1846/11/3 p.3) that Adams had rejected the Wartmannsightings as irrelevant55 to Neptune. To the contrary, Challis spent some telescope time56

50Challis did (M16:421) note the existence of the four other ephemerides. But he never publiclymentioned Hyp W (which was at the top of this very sheet of paper, CON #35[a]); moreover, he actuallydenied (fn 55) that its part-basis (Wartmann’s data) had anything to do with Adams’ predictions.

51 In fairness to Airy: there exists no evidence that he knew the details of Memo W (a secret provablyknown only to Adams & Challis).

52[Since Wartmann’s report turned out merely to be a fouled-up series of Uranus observations (fn 55),Kollerstrom notes that Adams’ top 1846 July solution (Hyp W) effectively confused the perturbedindicator with the perturbing quarry! I.e., Hyp W (top) inadvertently had Uranus perturbing itself.]

53DA (esp. §B4) showed that the traditional tale’s fall-guy, James Challis, was not primarily to blamefor England’s miss of Neptune. (Adams’ inconsistent directions were the main problem.) But I amtold that Challis’ miss is still today commemorated at the Univ of Cambridge, when unhappy Cantabstudents numb their woes by quaffing grog from a “Challis chalice”.

54Challis reported (Cambridge Chronicle 1846/10/1 and M16:423) that, during his 2nd of three9′-wide sweeps on the night of 1846/9/29 (just before news of Leverrier’s success reached England:London 9/30, Cambridge 10/1), he had noted one “star” (actually Neptune) as looking nonpunctal —and so asked his assistant to write there in the record: “seems to have a disc”. (DA fnn 27, 28, & 30analyze some peculiarities of this claim.) But the actual record (of which DIO possesses photocopies)actually commented in the past not present tense: “[last one] seemed to have a disc”. (The bracketedwords are scratched out.) See p.53 of Challis’ sweep book (part of CON). If he is to be believed, then:not only did he fail to engage the clock drive instantly to track and carefully examine the suspect object,but, at the end of the night’s 2nd sweep, he went straight on into a 3rd sweep — instead of spending afew minutes searching out the disc he allegedly had just seen. It was still well above the horizon.

55 The 1971 DSB (vol.3) Challis entry omits this intriguing part of Challis’ 11/3 letter: “Wartmann’sstar . . . Adams considered long since, and ascertained that if the observations are at all approximate,it must be much nearer the Sun than the new Planet.” (It is possible that this refers to post-discoveryconclusions from an internal evaluation of the Wartmann data. If so, Adams was right: the data are ofUranus. See P.Baum & W.Sheehan In Search of Vulcan NYC 1997 Chap.7 n.15.)

56Nights of 1846/7/30, 8/12, 9/21, 23, 28 (accounting for Hyp W’s 12◦ orbital inclination with nodec.130◦) and 9/3 (no inclination, thus near the far northeast portion of the search zone). Challis’ intenselooking into these areas might have no relation to Memo W, but spending serious time on far-eastsweeping was contra his realization that the far west region would be the first to become unavailablethis season due to the Sun’s gradual encroachment into the region. Indeed, considering that roughlyhalf of his sweeping occurred in the eastern half of the Airy-designated (CON #4 p.1, 1846/7/12) search


looking around the isolated & remote far-east regions predicted by Adams’ Hyp W. AndAdams’ Memo W ephemeris — top AND bottom — is temporally-centered upon the1846/8/29 date of opposition57 of the Wartmann-based Hyp W.

G Further Insight into Adams’ Large Misdirection of ChallisG1 Relative to where Adams was pointing (and how this relates to Challis’ miss ofNeptune), one of the most helpful documents is that of Adams to RGO 1846/10/15, inwhich he explains his erroneous extrapolation (from Hyp 1 & Hyp 2) to his final predictedorbit, Hypothesis X — which was sent by Adams to RGO on 1846/9/2.58 This is the crucialsolution which DR has been emphasizing for 30 years (e.g., Rawlins 1969), since [a] no otherhistorian has mentioned it, and [b] it is seriously wrong in longitude (longitude obviouslybeing THE key datum for searchers), over 10◦ west of the real Neptune, thus fatallymisleading Challis. (See fn 20 here; also DA §§B4 & F3.) Historians’ incomprehensionof the seriousness of the error is largely due to the fact that Adams expresses the resultas a mean longitude 315◦ for a virtually circular orbit. Unfortunately, most historians donot understand59 that null eccentricity automatically requires Adams’ final true longitude,Hyp X, also to be 315◦ — at a time when Neptune was actually at about 327◦. (Thepositions of the real Neptune and the several predicted planets of Leverrier and Adams areprovided in Tables 1&2 of DA for the entire first half of the 19th century.)G2 Therefore, the 10/15 letter must finally satisfy those who have found it incrediblethat: [i] Adams actually made such a huge mistake, and [ii] all previous historians havemissed this rather unsubtle slip. Those inclined to question the reality of the Hyp X error,will be enlightened by reading (§G3) Adams’ attempt60 to explain the very mistake they areevidently doubting ever happened. . . .G3 Fortunately, in the hitherto unknown contents of this private 1846/10/15 letter toAiry, Adams explicitly refers to his final solution (Hyp X), even giving its precise date(1846/9/2). His exact words (1846/10/15 to Airy, p.4, emph added):

In my letter of Septr 2nd, I inferred [DR: admirably correctly]61 that themean distance used in my first Hypothesis [Hyp 1] must be greatly diminished,but I rather hastily concluded that the change in the mean Long. deducedwould be nearly proportional to the change in the assumed mean distance.

[Note added 2011: precise extrapolation-math discovered at www.dioi.org/cot.htm#hpfp.]

area, it is odd that Challis explicitly stated that after 7/30-8/12, “I observed earlier [more westerly] inright ascension, for the sake of being able to go over in the present year as large a portion as possibleof the space to be explored.”

57The Hyp W planet’s opposition was at 5 AM of civil date 8/30, which was 8/29, 17h GMT, byastronomer’s (pre-1925) reckoning.

58Original in RGON; text published at M16:405-408.59 I am disappointed to see that Wm. Smart (quite knowledgeable in the relevant math) is so swept up

in his championship of fellow-Cantab Adams that he does not mention Hyp X (see Smart 1947 pp.21,29, 34) — or Adams’ own excuses for its considerable error. (See also Smart Celestial MechanicsLondon 1953 pp.253&262.) Instead he elects (idem) to promote only the pre-final two solutions (Hyp 1& Hyp 2), which were much closer to the mark. (Isn’t this a kind of switch?)

60The same excuse appeared at M16:456, in a part of his 1846/11/13 post-discovery presentationwhich no historian has cited (other than DIO: see DA §E8) perhaps partly because it is less clear (thanthe 10/15 letter) and does not explicitly cite the 9/2 letter (which DIO has said right along was thereference: idem).

61See DA fn 56. Note that in the 1846/10/15 letter and elsewhere, Adams proves far quicker andmore supple than Leverrier at realizing that both men’s elaborately perturbation-computed orbits wereflawed by their mutual initial assumption of the Bode’s Law distance 38 AU. In the full 10/15 letter,one can see Adams pressing his case that he had been wiser than Leverrier in this respect. I believethis is the best ground for defending Adams vs. Leverrier — however, it does not answer the questionof whether one ought to recognize post-discovery claims, especially after years of deliberate secrecy.


G4 I.e., Adams himself was fully aware that (in addition to several previous already-confusing longitude-predictions: fn 20) he had ultimately pointed Challis way off the correctlongitude for Neptune. So (as DIO has asked previously) why do Adams’ defenders62 ignorethis and pretend that his solution was good to roughly (or at least ordmag) a degree?G5 A further point relative to Adams’ final (Hyp X) solution: one of the most popularBrit alibis for losing Neptune was English nonpossession of the famous Berlin StarchartHour 21. Quite aside from our surprise discovery that, when the Cambridge search gotgoing, Neptune was moving conspicuously among the stars of Berlin Starchart Hour 22,which Challis had,63 we have also found that the ecliptical Hyp X solution was south of thesouthern limit64 of all the Berlin Starcharts. Airy’s 1846/7/12 letter to Challis (CON #4,perhaps unpublished before DIO) notes at p.4 that Hour 22 covers some of the suspectregion, but (he wrongly says) not much.65 Unambiguous upshot: map-alibi-byebye.

H Big Gaps, Big Eyes, and Perfect IdiocyH1 There are two suspiciously large gaps in the RGON record. Gap A: 1845/11/5-1846/6/26. Gap B: 1846/9/7-9/25.H2 Gap A is demonstrably artificial, since Airy’s 1846/6/25 letter to Whewell (RobSmith’s crucial find)66 is conspicuously missing. Moreover, we again (as DA noted) haveno information about Adams’ Neptune activities for a key period of more than a half-year.Sedgwick’s reference (12/6 p.2), to Adams perhaps getting bad advice (from Challis?)67 is

62 Virtually every popular history does so (sometimes just implicitly): [a] At the time of discovery,Leverrier was only 1◦ off. True. [b] Adams’ solution agreed with his to within 1◦. False for Hyp 1or Hyp 2 or Hyp X. As one sees from DA’s Table 1 for 1846/9/23: Hyp 1 & Hyp 2 were both 2◦ eastof Neptune, and 3◦ east of Leverrier’s predicted planet. Hyp X was 12◦ west of Neptune, 11◦ west ofLeverrier. Adams’ 1846 Sept solution (“Hyp G”) agreed with Leverrier almost on the nose (within atenth of a degree: DA §G9) — but that was Leverrier’s early (1846/6/1) solution, and Hyp G (becausebased on mismath: ibid §G4) is not the solution Adams later claimed he had given Airy in 1846 Oct(see idem), alleging that he had instead given him Hyp 1 (but without dating this legendary document).

63See Rawlins 1984N and DA fn 72.64DC §A6. The south bound of the Berlin Starcharts was declination −15◦ (epoch 1800.0).65On this (& Airy’s also-previously-unpublished 7/21 letter to Challis), see DA fn 72.66See Smith 1989 n.25.67 See fn 23. Challis’ official 1846/12/12 report just says (SP p.li) that in the crucial period between

1845 Autumn and 1846 midsummer, “I had little communication with Mr Adams respecting the newplanet.” [That Challis was actually in close regular contact with Adams during this very time (§H6)has been revealed by Kollerstrom, who finds: [a] The 1846/3/14 Adams diary entry (JCASJ) sayshe walked with Challis all the way to the Observatory even though not visiting it. [b] “Adams was[Challis’] own private friend” (Mrs.Airy to Sedgwick 1846/12/9).] But, then, Challis thought leavinga gap in the record was the only way out: §H10. Even former Chief Ass’t to the Astr Royal H. H.Turner was never allowed into the RGON file; see DB §C1 or Turner 1904 p.48 (“pinned”) and thus hisnon-awareness (ibid p.65) of Airy’s “shadow” sleight (fn 26 or DA §B2). But Turner’s intelligence wasjostled by central nonsense in the myth’s implicit assumptions. Turner 1904 pp.70-71: “Challis nevermade the most casual inquiry as to the result of [Adams’] visit to Greenwich which he himself haddirected Adams to make. I am judging [Challis] to some extent by default; because I assume the factsfrom lack of evidence to the contrary . . . . [Challis] never even took the trouble to inquire on [Adams’]return, ‘Well! how did you get on? What did the Astronomer Royal say?’ Had he put this simplequestion . . . and learnt in consequence . . . that this sensitive young man thought Airy’s [1845/11/5radial] question trivial, and did not propose to answer it, . . . . Even Challis might have been trusted toreply, ‘Oh! but you must answer the Astronomer Royal’s question: you may think it stupid, but youhad better answer it politely, and show him that you know what you are about.’ ” Though I disagreewith Turner’s interpretation, I am grateful for his carrying through, to show what bizarre scenariosone ends up with, by not facing the likelihood (DA §I10 item [2]) that, independently of Challis-Airy,Adams was himself (especially after catching his 1845 math error: DA §F2) paralysed into silence(fn 91) by his doubts regarding [a] the general trustworthiness of his math, and [b] the longitude that


the nearest thing to a recorded answer to this mystery. [See also fn 73.]H3 But we know that Airy-Challis-Adams met68 in early December, about the timeLeverrier’s 1st published memoir would have reached England, a temporal connection 1stpointed out in DA (§D4), suggesting Airy could’ve then warned Adams that Leverrier mightbe closing in on Neptune. In this context, one of DIO’s new findings reveals DA’s suspicionas too conservative: for, in fact, Airy knew of Leverrier’s work from the outset.69

H4 On 1845/9/22, Airy was at a meeting of the French Institute,70 and it was presumablythere that he learned that Paris Observatory chief F. Arago had deputed Leverrier, the mostcapable astronomer in the world (for this type of work), to eliminate the celestial offense ofUranus’ nontabular meanderings — a problem that particularly plagued Airy, whose veryjob it was to track the heavens accurately and who had already long since publicly brandedUranus’ intractability as intolerable (G.Airy Report. . . [BAAS 1831-1832] London 1833),echoing Laplace’s ultimate-theorist dream of banishing empirical terms from the heavens.Airy’s famous official public 1846/11/13 Royal Astronomical Society presentation actuallycites (M16:395) his attendance at the French meeting — but it does not mention what helearned there. (Recall the revelation of DA §E6 that, right after Neptune’s discovery — inearly Oct of 1846 — Airy also spied on Leverrier’s activities, by getting a pre-publicationlook at his prediction-math’s details, in the office of the Astronomische Nachrichten, wellbefore Adams had put a single digit of his prediction-math before the public. [See fn 69.])H5 This information guts the standard history, repeated now for 153y as if (well, whatare gaps for?) poor-naıve Adams never even knew of Leverrier’s work. How else excusetwo glaring glitches in BritMything: [a] Adams was silent for months even after Leverrier’s1846/6/1 paper. [b] Adams started work on Uranus well before Leverrier (somethingstressed by Adamsians when it suits their claims of priority) but ended up finishing71 afterLeverrier (see §B9). (Item [b] despite Adams’ crucial advantage that, entirely due to hissecrecy: he [& Airy, fn 69], not Leverrier, knew that a race was on.)H6 This central question was raised only once in the 1846 record we have when Sedg-wick asked Airy (1846/12/6 p.5; quoted by Glaisher at SP xxvi n.1 & Smart 1947 1947p.42) whether Adams had ever even been told that Leverrier was “at his heels”. AIRYNEVER ANSWERED THIS QUESTION. He implicitly pseudo-answered it in his incred-ible hardly-knew-him 1846/12/4 letter to Sedgwick: “My whole epistolary communicationwith Adams is printed in [M16]; and I never saw him but once somewhere with Challis (Itotally forget where) and once, when Hansen and I came for half a day to Cambridge and wewere walking across St. Johns’ bridge. The interview on each occasion might last 2 minutes.

would eventually result from it: §K2. Why else give top-of-page rank in Memo W to lost-star-basedHyp W (§F3), if he really believed his own math was firm, precise, and completed?

68 Question: at this 1845 Dec meeting (or when Adams & Airy were both at the 1846/2/13 R.A.S.meeting: fn 75), didn’t either man bring up the matter of the unanswered 1845/11/5 letter?! Anotherweird inconsistency relating to Adams’ incredible lost-period (which includes Gap A).

69 Airy to Arago 1845/9/29 referred to: “M. Le Verrier’s undertaking to examine the theory ofUranus.” (Also: “My calculations of some of Bouvard’s terms.” Which reminds us: Airy was one ofthe tiny handful of British astronomers who understood the math of the Uranus problem. See §H4 andDA §§E6-E7.) Not in NOAO copy of RGON, but faxed to DR by Elaine MacAuliffe, 1999/5/26.

70This is precisely the date of Challis’ famous letter of introduction of Adams to Airy. The match issubject to several interpretations. Prominently including, of course: pure coincidence.

71Adams claimed (RGON: 1846/11/18 to Airy) that he had little time except during vacations todo the Neptune work. However: [a] The unavailability of most of Adams’ diaries for the period inquestion prevents us from checking this. [b] Some of his 1845 work on Neptune was completed onApril 28. (See JCASJ W.16 §E II or Sampson 1904 p.165.) And in 1846 April, he delivered a paper(on another subject) at the R.A.S. (see DA §D1). (From these seasonal data, we can induce — partly byanalogy — that at least some of the time period between 1845/11/5 and 1846/9/2 was indeed availableto Adams for research.) [Additionally, the extant Adams 1846 March diary material shows that he wasdoing research work in several directions at this time — but nothing on Neptune. And there is thisremark under 1846/3/14: “Did not do much today, feeling rather tired. . . .”]


No other opportunity of seeing him.”72 [Note added 1999 Oct: Yet, Nicholas Kollerstromhas just discovered a portion73 of Adams’ diaries, 1846/3/9-3/28; Nick noted it shows that(during this supposedly-incommunicado period), Adams was in quite frequent touch withAiry’s close friend Challis (who knew all about Leverrier’s progress), and evidently waschecking some atmospheric refraction data of Airy.74 (All of which only makes the RGONfile’s Gap A look more incredible yet.) So the orthodox story that Challis & Airy were notcommunicating with Adams in this period appears to be just another smokescreen.]H7 And there is yet another (often inadequately separated) burning question put to Airyby Sedgwick in the same letter (also 12/3 letter pp.5-6): why Airy issued no immediatepublic cry in 1846 June when the Leverrier-Adams agreement was first realized,75 instead ofkeeping Adams’ prediction a “secret” (Sedgwick’s own word for it).76 Here, Airy did offer asort-of answer, in his 1846/12/8 letter (the one letter of the Sedgwick-Airy exchange whichAstronomer Royal H. Spencer Jones hid from Smart in 1946). But Airy never directly77

answered it. Both of 2 copies of Airy’s 12/8 letter were suppressed. (DA fn 12 had guessedit spoke “of Adams in extremely blunt terms”.) [Other copy now available in JCASJ. Soboth copies resurfaced near-simultaneously: §L8.] It’s part of the same Sedgwick-Airy1846 Dec set which Astronomer Royal Christie had (DC §A3) asked for censorship of.H8 [This letter’s heart was missing from the NOAO copy of RGON. But, at DIO’s1999/7/7 request, Nicholas Kollerstrom (University College, London), with RGO Archivist

72See RGON 1846/12/4 pp.1-2 (emph added), Smart 1947 p.40, or DA fn 75. Smart 1947 p.34(footnote) dates the 1st meeting to 1845 Dec 4-6; the 2nd, to 1846/7/2.

73 [Part of Adams’ 1846 diaries survives (fn 67), covering most of March, but nothing on Neptune:fn 17. The survival of just non-Neptune diary material, from a period so key to the Adams controversy,only adds to an impression that contra-myth documents have been knowingly filtered out.]

74 [See fn 67. Adams’ entire 1846/3/19 diary entry: “Gave some further developments to my[differential refraction] solution and worked some cases given by Airy.” Kollerstrom has also foundthat Adams and astronomer J. Hind were communicating during 1846 Feb (JCASJ), but not on Neptune;which may help explain why, after Neptune’s discovery, Hind expressed (1846/11/12 to R.Sheepshanks:Rawlins 1984N or DA §B5) such disgust for “the inexcusable secrecy” of “the Cambridge people [who]do their best for their own men.” Adams’ correspondence with Hind (who ran Bishop’s Observatory atRegent’s Park) bears on the myth that England’s Neptune fumble was due to Challis’ & Airy’s inertia.(Contra this, see Challis’ reasonable remarks at §B9.) But if Adams felt that Challis was too slow toact, then he could at any time have told Hind where he thought Neptune was. (Or other astronomers:Lord Rosse [see Smart 1947 p.46], W. Lassell, E. Cooper; all had access to major telescopes.) Hind,soon to become famous as Britain’s greatest asteroid discoverer, could’ve searched out the planet atleast as ably as Challis, and would probably have moved more nimbly on the project. (On 1846/9/30,Hind became the first Brit ever knowingly to observe Neptune, having just received a discovery-reportfrom the Continent.) But, then: Hind was not a Cantab.]

75 The standard Brit story implicitly tries to pretend (for why, see fn 68) that Adams & Airy had nocontact from 1845/11/5 until after the discovery. This laughable theory is refuted by their encounters of1845 Dec (§H3) & 1846/7/2 (§B11). (See also DB §G8: 1846/2/13.) A more intriguing hint: Airy said(M16:405) that in the late summer, Adams “was not aware of my absence from England” — yet theday, on which Adams posts allegedly the first letter he ever wrote to Airy (1846/9/2), was the last whenmail could reach Airy (who was vacationing: §I2) at Wiesbaden, which he departed 9/7 (M16:405).We note that Challis wrote Airy the same day (M16:405), also after a substantial silence.

76 See RGON Sedgwick to Airy 1846/12/6; essentially same question also in Sedgwick’s 12/3 letterto Airy (quoted at Smart 1947 pp.42 & 39, resp). Airy’s first claim that it was not his responsibility topublish Adams is in his 12/4 reply. (RGON p.4; quoted at Smart 1947 p.40).

77Some may say that an indirect answer was Airy’s 1846/12/4 (fn 76) and 12/8 (§H8) protests thatit wasn’t up to him to decide when to publish. (Irrelevant. See fn 91’s conclusion.) However: [a] Ifdistribution of Adams’ findings was up to Adams, then why was Airy in June telling Herschel, Whewell,Babbage, Peacock, etc? — but not the French or the public. (And were not Challis’ & Herschel’s1846/10/1 public letters taking right of publication from Adams? — which could as well have beendone in June. If Adams approved. Which is the whole issue.) [b] But such revelations in June wouldinstantly have triggered demands for Adams’ predicted longitude; thus, one is right back up against theflaw common to all Adamsian excuses: he had as yet no solution he trusted enough to make public.


Perkins’ willing help, recovered78 the letter’s startling center, revealing fully at last Airy’sprivate sardonic contempt for his detractors’ conception of events (and of ultimate blame).Replying to Sedgwick’s 12/6 letter, Airy simply created a spoof upon it:

I will put your propositions into the form, in which there is not the mosttrifling exaggeration.

Sedgwick’s Theory and Rules thereon founded1) Every Cambridge man is a Baby, and cannot walk out except he has a

Nurse to trot him out.2) Only Extra-Cantabs79 are eligible as Nurses. No resident, not even a

Plumian Professor [Challis], is competent to this office.3) Simple nomination of an Extra-Cantab by Baby imposes on such Extra-

Cantab . . . all the duties and responsibilities of Nurse.4) The regular duty of the Nurse is, to divine the unexpressed wishes of

the Baby to walk, and then to take him out.5) This responsibility of the Nurse is not removed even though the Baby

take a fit of the pique and refuse to answer questions, or though the Babyrefuse to clothe himself in what the Nurse considers to be a proper walkingdress.]

H9 As for Gap B, 1846/9/7-9/25. This hole is only broken by the 9/25 letter from BerlinObservatory Director J. Encke to RGO: “it is highly probable that Le Verrier’s planet isdiscovered.”80 Gap B may matter because Adams said on 1846/9/7 (RGON p.2, emphadded): “I hope by tomorrow [9/8] to have obtained approximate values of the Incl. andLong. of the Node, which I shall have great pleasure in communicating to you.” (Solutionsat JCASJ W.16 §G.)81 The italicized words were clipped off this quote when Airy publishedit (without ellipsis) at M16:408, and there is no 9/8 Adams letter in the RGON file. Didthe letter (assuming it ever existed) perhaps also offer a guess about longitude that wouldlook even worse than those of Memo W? Or did it express reservations about the wholeproject? Obvious innocent explanations exist here (e.g., fn 81); but, when a record has beenmanipulated for so long, dark speculations are invited. Again, natural human selectivity isexactly why post-discovery claims should (as a matter of policy) never be allowed.H10 There are other gaps. And those in logic exceed those in time. But, then, Challis’1846/12/19 letter to Airy said that Adams’ behavior in not publishing was so peculiar thatthe public would never understand, so “a hiatus must remain in the history”.

78[Kollerstrom was the first to make public the 1846/12/8 letter’s middle, which will forever beremembered as one of the most striking texts of the whole affair. Nick thus has the privilege of firstevaluation (1999/7/24): “My feeling is that Airy’s comments here are very fair and well-balanced. Thequestion which I suspect he never asked himself, however, despite his Proposition 3, is why he choseto accept the role of ‘Nurse’. I’d say this is the nearest Airy ever comes to expressing the Truth . . . .”]

79There is an unexpected implication here. DR has previously shown that astronomers such asHind scoffed at Univ Cambridge for nonpublication of its Neptune researches. But no one previouslysuspected that Airy (himself an eminent Cantab) was privately doing likewise — and (in hurt fromCambridge’s treatment of him) now counting himself as a non-Cantab.

80 “Highly probable” reflects an odd restraint; Encke, who knew orbit theory, previously doubted theexistence of Leverrier’s planet. (A fact Encke modestly never hid: C. Bruhns Johann Franz Encke . . .1869 p.303. Note: so Airy was not the only skeptical expert.) Encke goes on in this historic letter,fresh from the discovery-site: “Le Verrier by letter [arriving] 23rd Sept asked Herrn Dr Galle to lookfor it, and the same evening, during a comparison of the sky with the excellent academical Starchartof Herrn Dr Bremiker (Hora XX1), there appeared to Herrn Dr Galle an 8th magnitude star which wasnot found on the map. . . . By the 24th Sept, it had gone 1′ retrograde. . . . The motion agrees fully withLeverrier, so that this is a most magnificent discovery.” It was Encke who carried through Bessel’sSternkarten idea (fn 5), which aimed at helping to find new planets (Bruhns op cit pp.117-125).

81 Or Sampson 1904 pp.169-170. (See also Adams’ 1846/9/10&16 memos, misfiled in JCASJ under1843.) Adams got several large, disparate inclinations which may’ve discouraged his writing RGO.


H11 DA was the 1st Neptune history which drew detailed attention (DA §E3) to Adams’reluctance to publish his predicted elements (which would have required but two lines inthe following week’s Athenæum) even after Neptune’s discovery. Again, our remarks inDA (§§D6 & E) turn out to have been too conservative. In a vital RGON 1846/11/3 letter,Challis reports that, after well over a month of silence since the discovery, Adams is STILLreluctant to tell the public what he had allegedly been predicting for over a year. DA §E3noted the suspiciousness here of Adams’ apparent trouble in getting his story straight; nowthat we have found actual testimony about Adams’ reluctance to commit to anything, we arenot just speculating about his nervousness — a condition that does not enhance confidencein the reliability and non-selectivity of his eventual well-known 11/13 R.A.S. report. Whenthe person who stole the RGON file wrote the 1971 DSB article on Challis, he quoted thepart of the 1846/11/3 letter showing Challis’ reluctance to speak to the R.A.S. on 1846/11/13— but the part showing that Adams also looked likely to duck out was suppressed82 (seesimilarly at fn 55) and is only now being made known in this DIO paper.H12 Which segues us into the standard evasion of the simple (§B9) reality behind theAdams myth: his alleged naıvete. For, the revealing fact that Adams didn’t publish mustbe explained-away if one is to preserve the claim of Adams’ priority. But his total non-publication was inexplicable without frankly admitting the §B9 truth (a course which would,however, kill Adams’ claim to firstness); thus, one had to go to such alibi-extremes that, upto now, these recourses’ wildness has never been fully revealed. It got to the point wherethe loyalest important Cantab defender of Adams (Sedgwick) could only reply to Airy’sreasonable §H8 response (that Adams not Airy had to decide when to publish) by admittingAdams had behaved “very like a simpleton”. Or so Smart 1947 p.42 renders it. Butthe original of the letter (RGON) actually puts it more strongly: “like a very simpleton”.Question: when your top defender can only explain your actions by pleading you as aperfect idiot, can your case be regarded as credible? (See also fn 42.)

I Airy’s SlynessI1 No defender of Airy can convincingly explain away his keeping the French in thedark about Adams in his 6/26 letter83 to Leverrier (§B11). This was not square dealing (norwas his silence to Hansen: §B11); as Airy’s subsequent “desperate” (M16:403) steps show,he was scheming to grab Leverrier’s planet for England. And for Geo. Airy (§B11).I2 A previously-unnoted Airy ethical contradiction: he later said (M16:397) that, hadAdams replied to Airy’s now-famous 1845/11/5 letter of inquiry (§B8) about the Adamstheoretical perturber’s radial effects, Airy would have immediately helped Adams with allhis power. Well, Leverrier did reply (6/28) to the very same question — but Airy didn’thelp Leverrier a bit. (Quite to the contrary.) His public alibi (1846/11/13, M16:402) was

82 Same selective suppression at Smart 1947 p.38. Challis to Airy (1846/11/3, RGON file): “I amsorry to say that I can give no hopes of Adams’ being able to undertake the [R.A.S.] AstronomicalReport. He is moderator this year, & this, with his College duties, takes his time. I am in difficultyabout this Report, & should be glad to see some means of getting out of it.” (Smart and the DSB quoteonly the final sentence.) Challis’ witness to the fact that Adams (contra Adams to Airy 10/15 p.3)shared Challis’ reluctance to speak is plainly consistent with Adams’ weeks of glaring unwillingness totransmit a single number about his predicted planet to the public (§H11), to understandably-inquiringFrench scientists, or, indeed, to anyone outside his circle of Cantab conspirators — even while Challisand he were somehow able to find plenty of their precious time to fire off letter after letter to thepress (§B8) on, e.g., how to give a British name to the new planet. This is the standard hunkerers’lodge&dodge tactic (& see, e.g., conclusion of News Notes, above) a technique which enables itsemployer to: [a] lodge any story he likes, even while [b] dodging live cross-examination on it.

83Airy registered Adams’ work by his 6/25 letter to Whewell, which may be absent from the RGONfile since it makes Airy’s 6/26 silence to Leverrier look scheming. (DA fn 12 wonders if this silence wasdue to Airy’s learning on 6/26 that Adams was still-groping along, unsure of his math’s indications.)


that he was off on vacation to the Continent! This almost humorously incredible & boldexcuse neglects to explain how Airy managed (while speeding eastward for the Continent)to detour north to Ely (7/9) to conspire with Geo. Peacock and Challis (both of Cambridge),laying elaborate plans84 for catching Neptune ahead of foreigners and nonCantabs.

J Bloody Beak & Rank Lies: Airy’s Ire at Adams’ Worst AlibiJ1 When public rage at Airy was cresting in late 1846, Cambridge was abuzz with alie which had a natural appeal (see DA fn 52) to all those who sympathize with victimsof arrogant injustice. The lie (and that was Sedgwick’s blunt term for it, e.g., RGON1846/12/9) was that Airy had “snubbed” Adams in 1845 Autumn. As with alot of lies, itgot very fanciful — down to detailed allegations (Sedgwick to Airy 1846/12/6 p.1) thatAdams had an appointment at a certain time but was not received.J2 Airy could hardly believe the fantastic cast of these rumors. He was not in an upbeatmood to begin with: publicly portrayed as a liar by the French,85 his defense against Cantabanger was hobbled by his own ethically-inexplicable behavior towards Leverrier (§I). Ashe fought to survive a two-front war somewhat of his own making, his 12/8 letter, trying tostamp out dumb lies about himself, answers juster criticism by stonewalling: “here finishesmy Cambridge discussion. The next blow will probably be from Paris.” He’d alreadyresigned himself to being abused (12/4 p.1), wryly quoting an ancient warning:“Those who in quarrels interpose / Must often wipe a bloody nose.”J3 Smart 1947 p.42 had quoted Airy-to-Sedgwick at this tense time: “I must have avery low opinion of those who have so taken it up that my old friend [Sedgwick] has felthimself obliged to question me as if I were a criminal”.86 DA launched the new theorythat Airy was referring to Adams. The full RGON file (though superficially ambiguous)87

contains strongly worded evidence (§J8) encouraging this view.J4 Sedgwick’s letters tried to convince Airy that Adams had no role in starting theserumors. Airy knew better. But as a canny politician he also knew better than to counterattacka hero in public, no matter whom the facts actually favored. However, Airy knew the awfultruth all along — and he knew it more reliably than anyone has previously suspected.J5 For, his brother Wm. Airy was reporting directly and specifically to him all of theanti-Airy rumors got up at Adams’ college, St. Johns. Even months after the discovery,Wm. Airy writes his brother (RGON 1846/12/9):

When I was at Cambridge last week I heard so much about the new planetthat I actually dreamed about it. You are aware, I know, that the Johnianshave taken up the cudgels against you for “snubbing” Adams . . . . the charge

84Details summarized in DA (e.g., §B4) or M16:404. Main plan elaborated in Airy’s 1846/7/12 letter(CON #4) to Challis.

85 Leverrier (1846/10/16) asks — quite reasonably — how Airy could claim England had the slightestconvincing priority (or even capability for it) when Airy had had to ask Leverrier (6/26) about the radialeffect of the predicted planet. He evidently wondered if the Brits made up the whole story. Evidencecontra this idea cannot be found in any continuous record: DA §I9. [And see fn 73.]

86 Airy’s skill at fending off embarrassing questions with a how-dare-you pose helped him survive— but it does not help his credibility with an historian.

87Some may dispute DR’s interpretation here, so I give full contrary data. Airy’s 12/10 letter endsby making peace with Adams, which politician Airy knew he had to do. But the RGON file containsrepeated evidences (fn 89) known to Airy: [a] that Adams was the source of the “snubbing”-rumor(as if one even needed evidence on such an obvious point, after all, who else had a motive to tellsuch a lie?), and [b] that Adams, even as he finally tried to find innocent explanations for Airy’s 1845Oct unavailability, harbored a deep and almost inoperable regret-resentment over not seeing Airy onthat 2nd visit to RGO. Thus, Airy’s most private remarks (first revealed to the world in this paper:§J8) express no forgiveness towards Adams and instead contain a crisp and intelligent summing-upof the whole discreditable Adams-circle slander, a lie that has continued into modern histories, e.g.,DA §E7. [Note added 2017/6/18. For a gauge of Airy’s political hyper-sensitivity, see Diego Medan’sunexpected finds (in a long-neglected trove of Arago material) at [email protected].]


was stated by Babington of St. Johns (a friend88 I believe of Adams) either inTrinity Combination Room, or at Sedgwick’s rooms on Audit night.

J6 And no denial by Sedgwick (or anyone else), of Adams’ involvement in startingthese rumors, could erase from Airy’s memory the remarks Adams had made in a recentpart-apology part-alibi letter (11/18 p.3) to Airy himself, saying that Adams was “muchpained”89 at not having been able to see Airy during the legendary failed visits to RGO in1845 Autumn. Adams initially (later retracting) blamed Airy not with vicious intent,90 butrather in quite natural disappointment (at missing out on a unique discovery) — abetted byan equally natural if unadmirable delusion that someone else was the problem.J7 Airy’s rage peaks in his 1846/12/8 letter to Sedgwick. Again, this is the very letterthat DIO indicated (DA §A6 and DC §§A3&A5) was deliberately suppressed. [It is nowfinally public in full (§H8) thanks to the honesty of Nick Kollerstrom and Adam Perkins.]Airy’s charge (§H8) was so strong that Sedgwick (12/9) called it “ludicrous”. (But he hadnot seen Adams’ unqualified 11/18 blubbery wail-tale: §J6.)J8 Airy’s view of Adams is suggested by a newly revealed 12/11 note to brother Wm.:

The Johnian story to which you allude was a capital example of the sort ofconnivance among associated persons which produces rank fibs. Sedgwickwent thoroughly into the matter and at length produced the final retraction ofthe story.

J9 Airy’s fury subsided when old-friend-intermediary Sedgwick confronted Adams andat last got him to admit frankly his own blame (for not answering Airy’s 1845/11/5 letter— said letter being Airy’s does-this-look-like-a-snub? trumpcard91 when answering Sedg-wick). Airy then magnanimously if toothgrindingly tells Sedgwick (1846/12/4) he’ll be

88He too (like Adams) was forced by Sedgwick to retract the falsehood that Airy had snubbed Adams:Sedgwick to Airy 12/6. [Adams’ diary entry of 1846/3/12 mentions a Babington.]

89 Also Adams’ 1846/12/6 remarks to Sedgwick (as he reported in his letter to Airy of that day,finished on 12/7 and postmarked then): “(1) He called at the [Royal Greenwich] Observatory soonafter his calculations were finished — the Astronomer Royal away — Bad luck [DR: though, seefn 67 & DA §H4], but no blame anywhere — this was Sept. [1845] — (2) Called again (Oct. thesame autumn) & the Astronomer Royal out — left his card — told that Airy would return soon, &therefore left word that he would call again — (3) Did call again (I think in a little more than an hour)& was told that the Astronomer Royal was at dinner & had no message & therefore went away . . . .added he did not call by appointment — He only took his chance on his way back from Devonshire toCambridge . . . . I collected that he had been mortified (I am not using his own words) at receiving nomessage on the second call in October —.” Emph in orig. The letter continues (the quotation-marksnow become Sedgwick’s, as he quotes Adams directly): “I thought . . . that though he [Airy] hadbeen at dinner he could have sent me a reply, or perhaps spoken a word or two to me: but I am nowconvinced that he never knew of my second call — that the servant had not delivered my message alongwith my card —” Sedgwick goes on in his own words: “I asked him [Adams] whether [this incident]had any influence in preventing his reply to Prof. Airy’s [1845/11/5] note. He said in answer, thathad these not happened he possibly might have replied more readily . . . .” (Smart 1947 has alreadypublished excerpts from these exchanges, though he could only guess about the most important letter[1846/12/8], since it was kept from him; also from J.Glaisher earlier: SP xxvi-xxvii.)

90Which is partly why Airy forgave Adams (& see §J4). Also, Airy valued Adams’ rare intellect.(And modesty: see the lovely tale at Smart 1947 pp.16-17, justly ranking Adams as “a prince amongSenior Wranglers”.) Adams’ rumors may’ve started defensively: as early as 1846/10/10, he was told(by friend E.Spencer, JCASJ 14/15/3) that Airy was laying “the whole blame upon your shoulders”.

91 But it doesn’t tell us why Airy didn’t ask Adams about the 1845/11/5 question at their three knownpersonal encounters [see also Kollerstrom’s recent find in Adams’ diary: §H6)] between then and thediscovery (fn 68 & fn 75: 1845/12-1846/7/2). The obvious reason? Adams was going back over,shoring up, and extending his work — so he had no firm solution for Airy until later (fn 20: 1846/9/2).But openly admitting this would end Britain’s priority-claim, so the ridiculous implicit contradictionpointed out at the beginning of this footnote had to stand (actually hide: no pre-DIO account has even


glad to receive Adams — even while gloating that Adams had been “trounced” enough(over his nonresponse to Airy’s 11/5 letter) to put him in his place.92

J10 So Airy survived — and (just as Adams finally rose to the heights of theoreticalastronomy: see DA’s happy conclusion), Airy went on to be one of the great figures in thehistory of astronomy, that rare able administrator who was also a top-notch theorist. (Thetwo types rarely combine, pioneer physicist Arago being a particularly sad example of thenorm: though he was Leverrier’s 1845 deputer and intensely loyal 1846 champion, he fellfrom power a few years later — at Leverrier’s own hands.)

K Tale-ReductionSumming-down our newly-informed view of the Neptune-chase history, one can say thatpreventing the old mythty-eyed tale from leading one astray requires only that one not losesight of the indisputable key truths:K1 Adams deliberately, repeatedly, systematically kept his results secret from the world.His later defense, told to Sedgwick (relayed93 to Airy 1846/12/6), was almost funny: thattelling a fellow-secrecy-conspirer constituted the equivalent of publication.K2 As already noted at §B9 & fn 20 (from DA), Adams’ alibis are each demonstrablyeither irrelevant or false. The truth is simple but is too unromantic for writers to like: whilejumping about with various predicted longitudes (fn 20) for Neptune, Adams couldn’tfeel confident of Neptune’s place94 UNTIL HE VARIED THE MEAN DISTANCE (in hisrigorous perturbation math: Hyp 2 vs Hyp 1), and he did not send the result (Hyp X)to RGO until 2 days after Leverrier’s last paper was already published. This (perhapsreasonable) caution — and maybe also Adams’ (ironically backfired) desire to sneak amarch on Leverrier by not even telling him that they were racing95 — is all there ever wasbehind Adams’ hitherto-mysterious publication-delay, a delay which created both the non-pinpoint-prediction disaster and the pinpoint-prediction myth of Adams’ miss of Neptune.

remarked the contradiction) in the place of honest history. (Note resemblance to fn 67.) Obviously,(but see fn 51), Airy was, at some point before 1846 Sept, aware of Adams’ math block, unless weassume (as incredibly, the standard history has implicitly assumed) Airy set the largest UK refractor onthe most intensive sky search ever up to that time without consulting (at least via Challis, with whomAiry was in dense correspondence) the next-door Cantab mathematician whose work co-launched thewhole project. NB: Adams’ non-reply is no excuse for incuriosity now regarding his research’s status.

92Airy to Sedgwick (RGON 1846/12/10 p.2) comments on the latter’s recent questions, which “nogentleman if free would ask and which no gentleman could be expected to answer. . . . I am nowperfectly satisfied with what you have done . . . . But never let me see the low fellows who have causedit. With Adams, I have no quarrel whatever (he acted discourteously in not answering my [1845/11/5]inquiry, but he has been much trounced for it and so that is over) and I shall be glad to see him atany time.” Note that the Adams-circle’s ridiculous and refutable slanders against Airy allowed him toconcentrate his fire where he was genuinely wronged — and, having shamed Sedgwick a bit, Airy wasthus eventually able to distract Sedgwick from the points where Airy himself had behaved badly: §H8& §I. Airy finally resorted to the ultimate ploy of the cornered: he shut off discussion: §J2 & fn 86.

93 According to this letter (12/3 p.3), Adams told Sedgwick that he had “done my best” in sendinghis results to the two national observatories and had assumed Airy had told colleagues about his results.(See fn 42 and Airy’s convincing rejoinder [RGON 12/4 p.3 or Smart 1947 p.40]: Adams’ non-replyto Airy’s 1845/11/5 inquiry shows that Adams “did not do his best”.) Yet Adams’ own failure tomention his research to the R.A.S. (DA §D1) or to speak up when he met (above: §B11) the greatcelestial mechanist P. Hansen (whose equations Adams was using!) shows that he took a share in theCantab-circle secrecy [see also fn 74] — which cost him a share in the planet.

94 [Adams’ constant companion (fn 67) Challis believed that in 1845, Neptune’s “position wasdetermined but roughly” by Adams’ work (§B9). Possibly Adams was only inspired by Leverrier (his1846/6/1 paper) to perform a solution using a mean distance other than the Bode value 38 AU.]

95See §H5. Leverrier & Adams raced to be the first to achieve a solution independent of a pre-assumedmean distance. Leverrier finished in August and published 1846/8/31. Adams sent his solution to RGOtwo days later. (DA §D5 suggests a possible causal connection, though see fn 75.)


ReferencesSame as in DA & DB [p.4’s abbreviations], but with these additions:

RGON file = Royal Greenwich Observatory Neptune file.96

JCASJ = John C. Adams papers,97 St. John’s College (Cambr), cited by box/folder/item.DA = D.Rawlins 1992W. DIO 2.3 ‡9.DB = D.Rawlins 1994N. DIO 4.2 ‡10.DC = DIO 7.1 ‡5 §A.

L Note Added 1999 OctoberAs the clenchjawed Brit establishment attempts (e.g., fn 2) to cope with the ghastly

disaster of public vindication of DIO’s charge98 (published nowhere else) that RGO’s recentpenultimate high official stole the RGON file, the inevitable establishment alibis (e.g., §C7)are even now building. A warning: If the establishment gets the have-cake&eat-it ideathat it can tuck away embarrassing key archival data for decades and later pay no price, byshrug-pretending it was all a mixup (similar case at DIO 10 �1), then no file or historicaltruth will be safe. And the RGON file’s long disappearance was no accident:L1 The theft undeniably occurred close to the time when an openly skeptical scholar(DR) asked to see the RGON file.L2 The file had topsecret status long before the RGO official in question was even born.(See, e.g., fn 67.)L3 The filching official himself said (§C7 item 4) that he got into the Neptune case byrequest and as part of his official RGO duties. For this reason among others (fn 26), it isobvious that Astronomer Royal Woolley knew who had the file.L4 Are we to believe that when Woolley was asked (by DR) to see this sensitive file, itis purely coincidental that the person who hid it was his closest colleague? (The Henry II-Becket who-will-rid-me parallel [earlier Brit history] is almost too obvious.) See §C2.L5 Photocopy machines were common in the 1960s, so there was no need for a researcherto remove a whole file of original mss.L6 Not even a copy of the 1967-promised RGO list of the file’s contents was everforthcoming (see fn 29 and §L9).L7 All 1960s RGO letters to DR regarding the “missing” file were (§B13) on privatestationery, while letters on other matters were on official RGO stationery.L8 Copies of the long-hidden full Adams-Sedgwick exchange have existed all along inJCASJ, though for over a century this file’s letters were largely uncataloged (and thereforeunaccessible, as DR learned during a 1996 Sept visit). But in 1998 Nov, right after theRGON file fell into foreign hands, the project of organizing them was begun (& rapidlycompleted by E. Q. Lawrence). So both copies of the key 1846/12/8 letter reappeared withimpressive simultaneity (§H7): within a time ordmag 1/1000 the size of their secrecy-spans.L9 During the brief period (1967) when RGO acknowledged to DR (DB §E10) that ithad the file, RGO was making up a list of selected “letters for examination” (DB §E11) —i.e., it was preparing to hide the most embarrassing letters (just as had been done beforeWm. Smart saw part of this material in 1946-1947). In brief, censorship was the 1960s RGOpolicy regarding these documents; and the file’s disappearance at this very time displays aconsistency (with that suppressive mentality) which is pathetically obvious.

96Originals at University of Cambridge Library. Microfilm available (tel 44-1223-33-3056, AdamPerkins). Copies can also be made by NOAO in Tucson, AZ (tel 520-318-8295, Mary Guerrieri) orNOAO in Cerro Tololo (tel 56-51-225-415, Elaine MacAuliffe).

97We are indebted to Kathryn McKee (Technical Services Librarian, St. John’s College) for faxingnew material from this source — and to Nicholas Kollerstrom for alerting DIO to its sudden availability.

98See above at §B14; original publication in DA §C 5 (1992) & DB §H6 (1994).

26 1999 June DIO 9.1

‡2 Evidence of an Ecliptical Coordinate Basis in theCommentary of Hipparchos

by KEITH A. PICKERING1

A Hipparchos’ Spherical-trig SlipA1 The only surviving complete work of the Greek astronomer Hipparchos (2nd centuryBC) is his Commentary on Aratos and Eudoxos, which contains several hundred partialpositions of stars. These positions are expressed in a manner that is quite different frommodern forms. For example, Hipparchos will state that a star rises at the same time as acertain degree of the ecliptic rises, or that a star sets at the same time as a certain degreeof the ecliptic rises. Positions of this type are collectively referred to as “phenomena.”The most common phenomena are those where Hipparchos states that a star culminates(i.e., transits the meridian) at the same time as a certain degree of the ecliptic culminates.There are over 200 stars described this way in the Commentary — many of them more thanonce, and frequently with different (conflicting2) results. These simultaneous culminationphenomena he called “mid-heaven” phenomena; here, we call these data "polar longitudes."A2 There is now ample evidence that the Ancient Star Catalog (ASC) preserved in theAlmagest of Claudius Ptolemy (2nd century AD) was in fact plagiarized3 from Hipparchos,after adding 2◦40’ to the longitudes for precession. But contra these evidences, somebelieve that because the Commentary (unlike the ASC) contains no star positions in thestandard ecliptical reference frame, that Hipparchos did not take ecliptical positions —and therefore could not have been the true author of the ASC. So if it can be shown thatHipparchos did in fact take ecliptical positions of stars, the case for his authorship of theASC becomes even stronger.A3 Not much is known about how Hipparchos obtained the data in the Commentary.It has been frequently assumed, on the basis of comments by Ptolemy, that Hipparchosused a celestial globe to chart his star positions, and may also have used the globe toperform spherical coordinate transformations. However, if Hipparchos used an armillaryastrolabe to obtain star positions (and even this has been disputed by Neugebauer), a muchsimpler method is available. After sighting the star through the pinnules of the astrolabe,Hipparchos simply rotates the astrolabe (around its equatorial axis) until the pinnules are inline with the astrolabe’s horizon ring. The astrolabe now is in a position that represents thesky at the time of the star’s rising (or setting), and Hipparchos can simply read the positionof the ecliptic ring against the eastern horizon ring to get the degree of the ecliptic that risesat the same time as the star. Since the ecliptic ring is not directly adjacent to the horizonring, however, the result necessarily will be rougher than the star’s ecliptical position; andindeed, the positions in the Commentary are recorded only to the nearest half-degree, aboutthree times less precise than the positions in the ASC.A4 But there is another possibility: if Hipparchos observed and recorded the starsecliptically, then the positions in the Commentary could have been derived by using sphericaltrigonometry. This is especially true of the polar longitudes, because while the spherical

1 Analysts International Corporation, 3601 W. 76th St., Suite 200, Minneapolis, MN 554352 This despite those apologists for Ptolemy who claim that “standard ancient practice” forbade

publishing multiple discordant data for a given phenomenon.3 Newton 1977, 211-256; Rawlins 1982; Rawlins 1994.

K. Pickering Hipparchos’ Stars: Ecliptical Base 1999 June DIO 9.1 ‡2 27

trig conversions for rising and setting phenomena are cumbersome (and differ by latitude),the spherical trig required for polar longitudes is fairly straightforward.A5 Obviously, a polar longitude is simply a different way of expressing the right as-cension α of a star. Converting ecliptically-observed coordinates into a polar longitude isa two-step process: first Hipparchos computes the star’s α from its ecliptical latitude andlongitude. Then he finds the degree of the ecliptic that has the same α. This second stepwas probably done tabularly, and need not have been done at the same time as the first step.A6 Although the suggestion of spherical-trig conversions may seem speculative, thereis evidence in the Commentary that this is exactly how the polar longitudes were derived, atleast in some cases. This is because sometimes, in making these conversions, Hipparchosslipped up. In the second step of the process, Hipparchos is supposed to find the star’sα in a table, and read across to find the degree of the ecliptic with the same α. Butoccasionally, instead using the star’s right ascension α for the lookup, he would use thestar’s ecliptical longitude λ by mistake. Since α and λ usually have similar values, thiserror is not immediately obvious.A7 The clearest case in which this error occurred is that of 32 Cygni, which is listedin the ASC at latitude β = 64◦30′, longitude λ = 302◦40′. After subtracting 2◦40’for Ptolemy’s incorrect precession, Hipparchos’ observed longitude becomes λ = 300◦.Hipparchos converted to equatorial coordinates to get α = 287◦, a value which he notesin his catalog. (Or, following the intelligent suggestion4 of Grasshoff 1990, this wasmore likely a working proto-catalog from which both the Commentary and the ASC werederived.) But at this point the α is inadvertently dropped. Looking under the wrong column,Hipparchos used 300◦ (rather than the correct 287◦) to look up the degree of the eclipticneeded for the mid-heaven phenomenon, and arrived at 298◦, the exact value that appearsin the Commentary. If Hipparchos had not slipped in step 2, he would have arrived at (afterrounding) 285◦30’ for the polar longitude of 32 Cygni. The resulting twelve degree erroris one of the largest of all polar longitudes in the Commentary.A8 Finding all such errors in the Commentary turns out to be rather easy. First, weconvert the ASC back to the epoch of Hipparchos by subtracting 2◦40’ from the longitudes.We then use these positions to compute α for each star with a polar longitude in theCommentary5 (using the Hipparchan obliquity of 23◦40’), and determine the “correct”polar longitude. We compare our computed polar longitude to the values given in theCommentary to determine the true error T . Next, we recompute the polar longitudesassuming Hipparchos actually made the λ-for-α slip described above. We compare ourrecomputed polar longitudes to the values given in the Commentary to determine the “slip-up” error S. If Hipparchos did not make a mistake, error T will be small and error S willbe large; but if Hipparchos made the λ-for-α mistake, T will be large and S will be small.Therefore, dividing T by S will produce a very small number if the mistake was not made(which is usually the case), but a large number if the mistake was made. We plot thesevalues in Figure 1 for all 273 polar longitude data in the Commentary, representing 203stars. For convenience, we use the ecliptical longitude as the x-axis, and plot the absolutevalues of T/S on the y-axis.A9 While most of the data hug the x-axis, a few discordant stars leap to attention. It isnow easy to see that there may be several cases in which Hipparchos made this mistake.To determine if these are just statistical flukes, we need to find the probability that T/Sis greater than a given value V . First we find the mean µ and standard deviation σ ofall T and all S in the population. These are: for T , µ = −0.05, σ = 4.95; and for S,µ = 3.72, σ = 23.72. Next, assuming that T and S are normally distributed, we find theprobability that T is outside of a given range ±t, and multiply by the probability that S

4 Grasshoff went out on a limb suggesting that Hipparchos’ catalog was ecliptical in nature, so it issatisfying to see his courage vindicated here — a sentiment shared by the author (KP) and publisher(DR) of the present paper.

5 Grasshoff 1990, Appendix C.

28 K. Pickering Hipparchos’ Stars: Ecliptical Base 1999 June DIO 9.1 ‡2

Figure 1: Parameter T/S plotted by longitude.

is inside the range ±t/V . (As it turns out, in this case the probability is maximized whent = 3.72, regardless of V .)A10 We find that in a population of 273, we would expect to find 1.1 cases whereT/S > 14 (probability = 4.0 × 10−3); but the Commentary actually has four. And weexpect only 0.36 stars where T/S > 42 (probability = 1.3 × 10−3); the Commentary hasthree. This makes it quite likely that these three cases are not random. These cases are 32Cygni, λ Leonis, and ζ Ophiuchi; the details of each are given in Table 1 below.A11 It is important to note that there are two requirements for this type of error to occur.First, Hipparchos must have had the ecliptical positions recorded in his proto-catalog. Andsecond, Hipparchos must have converted these positions using spherical trig; this type oferror is simply not possible using a globe or an astrolabe as an analog computer.

Table 1. λ-for-α error candidates.

Name λ β α Apl Spl Cpl T S T/S32 Cyg 300 64.5 287.0 285.7 297.9 298 12.3 0.1 108.3ζ Oph 219.5 11.83 220.8 223.3 222.0 222 1.3 0.0 42.2λ Leo 108.5 7.5 111.3 109.6 107.0 107 2.6 0.0 53.2

λ = longitude from the Almagest – 2◦40’; β = latitude from the Almagest; α = RA computedfrom λ and β, using 23◦40’ obliquity; Apl = polar longitude computed from α; Spl = polarlongitude assuming the slip occurred; Cpl = polar longitude given in Commentary; T = ab-solute value of Apl – Cpl; S = absolute value of Spl – Cpl.

K. Pickering Hipparchos’ Stars: Ecliptical Base 1999 June DIO 9.1 ‡2 29

B Theta GeminorumB1 Another interesting proof of Hipparchos’ use of ecliptical coordinates (and of Ptol-emy’s theft) is the case of θ Gem. This star was observed by Hipparchos with eclipticalcoordinates using an ecliptical astrolabe. Hipparchos’ originally observed coordinates werevery likely λ = 71◦, β = 10◦, a position within a degree of correct in both coordinates,which is not atypical. (The fact that both of these are integers is the dead-giveaway forecliptical observation.)B2 But soon after this number was written down, a scribal error was made by Hipparchosor one of his assistants. In ancient Greek, the numeral 1 (uncial alpha) closely resembles thenumeral 4 (uncial delta), and this is the most common6 number confusion in many ancientGreek astronomical texts. So while the longitude 71◦ was observed at the astrolabe, and waswritten on an observational note, the number 74◦ was recorded in the proto-catalog, a hugethree-degree error. Since this is several standard deviations above the mean Hipparchanerror, it is a firm indication of a scribal slip.B3 Hipparchos proceeds as before: converting his (incorrect) ecliptical coordinates toright ascension, he gets 71◦.2; then he converts a to polar longitude, getting 72◦.7, whichis also three degrees too high because of the scribal error. He rounds7 this to the nearestinteger as 73◦, the number that appears in the Commentary.B4 Then near the end of his career, Hipparchos again read the erroneous 74◦ positionfrom his proto-catalog and published it in his final star catalog. Three centuries later,Ptolemy adopted Hipparchos’ longitude of 74◦, added 2◦40′, and arrived at 76◦40′, thevalue he published in the Almagest. If Ptolemy had really observed θ Gem himself, hecould not have gotten a result this bad — not even with repeated observation, the commonexcuse of Ptolemy’s defenders regarding his planetary fabrications. And in Ptolemy’s case,no write-1-read-4 scribal slip can be invoked, since his longitude contains neither a 1 nor a4.B5 We also know in this case that the polar longitude cannot have been the originalobservation, in the following way. Suppose that the polar longitude was the originalnumber and the ecliptical coordinates were derived from it. In that case, starting witha polar longitude of 73◦, Hipparchos would have gotten a Right Ascension of 71◦30′.Combined with the latitude 10◦, this would have given an ecliptical longitude of 74◦15′

(after rounding to the nearest fraction in the ASC). Ptolemy would have added 2◦40′ tothis, getting 76◦55′, which he would have rounded to 77◦: a full 1/3 degree higher than thelongitude (76◦40′) that actually appears in the Almagest.B6 So the polar longitude can be derived from the ecliptical coordinates, but the reverseis not true: the ecliptical coordinates cannot be derived from the polar longitude. Thereforethe ecliptical coordinates must be original, and the polar longitude (which appears in theCommentary) must be derived from them.

References:

Grasshoff, Gerd (1990). The History of Ptolemy’s Star Catalog. Springer-Verlag.Newton, R. R. (1977). The Crime of Claudius Ptolemy. Johns Hopkins University Press.Peters, C.H.F., & E.B. Knobel (1915). Ptolemy’s Catalog of Stars. The Carnegie Institutionof Washington.Rawlins, Dennis (1982). An Investigation of the Ancient Star Catalog. PASP 94, 359.Rawlins, Dennis (1994). Hipparchos’ Sites. DIO 4.1, 33.

6 Peters & Knobel 1915, 9.7 Note that if Hipparchos had rounded to the nearest half- degree, as often occurs in the Commentary,

he would have gotten a polar longitude of 72◦30

′. Why he sometimes rounds to halves and sometimesto whole numbers remains a mystery.

30 1999 June DIO 9.1

‡3 Continued Fraction Decipherment: the AristarchanAncestry of Hipparchos’ Yearlength & Precession

The Aristarchos Sidereal Year’s High AccuracyHis pre-Hipparchos Knowledge of Precession

Consistency & Cause of Greek Tropical Year’s Error

[Eighteen years ago, this paper was doubly refereed & accepted for publication by theJournal for the History of Astronomy but was then suppressed for its §E heresy on Ptolemy.(Details below at §F.) Substantial changes & additions to the 1981 version are in brackets.]

A IntroductionA1 Not long ago, Neugebauer republished and considered a couple of largely undeci-phered lists1 (see Table 1) of ancient values for the year’s length, taken from the VaticanGreek mss collection.A2 He comments2 on the mysterious state of the numbers:

The first number is the traditional value for the Greek version of theMetonic cycle. The remaining numbers are obviously corrupt; the numberof Aristarchus in [list] A could perhaps be rescued by interpreting ξβ′ as[sixtieths of the second power] i.e. “seconds,” but the resulting 365;15,20would still leave [the Aristarchus year in list] B unexplained, nor is there anyrelation to another supposedly Aristarchean value 365;15,2,13, . . . [365d1/4+ 3/4868 or 365d1/4 + 1/(1622 2/3)].

[The previously puzzling digits of the mss are rendered in both Greek and Arabic in Table 1.]

B SolutionsB1 I have elsewhere already shown3 that Eratosthenes’ famous value for the obliquity(c.200 B.C.), 11/83 of a semicircle (23◦51′20′′), is derived from a continued-fractionprocess (upon his empirical result, 23◦51′15′′).4 And I find that others5 have suspected thatthe continued-fraction technique (for approximating any number by a rational expression,as closely as desired) goes back at least as far as Eratosthenes’ Alexandrian predecessor,Aristarchos of Samos (fl. 280 B.C.).

1Otto Neugebauer, History of Ancient Mathematical Astronomy (3 pts, New York, 1975), p.601.Lists published earlier by W.Kroll and E.Maass. Neugebauer (loc. cit. note 1) gives detailed citations,including the information that list A is from Vat. gr. 191 fol. 170v; list B, from Vat. gr. 381 fol. 163v.

2Ibid., 601-602.3 For details, see Robert Newton, “The Sources of Eratosthenes’ Measurement of the Earth”, Q.

Jl Roy. astr. Soc., xxi (1980), 379-387, pp.386-387; or [Rawlins, “Eratosthenes’ Geodesy Unraveled”Isis, lxxiii (1982), 259-265, pp.262-263. See also DIO 2.1 ‡3 fn 26.]

4Almajest (henceforth [usually] abbreviated Alm.), I 12.5Starting with Fortia d’Urban. See Thomas Heath, Aristarchus of Samos (Oxford, 1913), 336, and

Greek Mathematical Works [Loeb C L], English translation by Ivor Thomas, ii (London, 1941), 14-15.

1999 June DIO 9.1 31

Table 1: The Vatican Mss Lists of Ancient Yearlengths in Days

List A:

Calendarist Manuscript DataMeton, Euktemon, Philip 365 5/19 365 5/19Aristarchos of Samos [365] 1/4 κ′ ξ β′ [365] 1/4 20′ 60 2′

Chaldeans 365 1/4 ε′ ζ′ 365 1/4 5′ 7′

Babylonians 365 1/4 1/144 365 1/4 1/144

List B:

Calendarist Manuscript DataEuktemon, Philip, Apollinarios 365 5/19 365 5/19Aristarchos of Samos 365 1/4 ι′ δ′ 365 1/4 10′ 4′

Babylonians 365 1/4 ε′ ζ′ 365 1/4 5′ 7′

Sudines 365 1/4 γ′ ε′ 365 1/4 3′ 5′

———– 365 1/4 ρ′ σ′[ 365 1/4 100′ 200′?

Table 2: Continued-Fraction Interpretations of Table 1’s Data

List A:

Calendarist Year Continued Fraction Restored YearMeton, Euktemon, Philip YE 365 1/(4 − 1/5) 365 1/4 + 1/76Aristarchos of Samos YAt 365 1/(4 + 1/(20 + 2/60)) 365 1/4 − 15/4868Chaldeans YBt 365 1/(4 + (1/5 − 1/7)) 365 1/4 − 1/c.285Babylonians YBs 365 1/(4 − 1/(9 + 1/4)) 365 1/4 + 1/144

List B:

Calendarist Year Continued Fraction Restored YearEuktemon, Philip, . . . YE 365 1/(4 − 1/5) 365 1/4 + 1/76Aristarchos of Samos YAs 365 1/(4 − 1/(10 − 1/4)) 365 1/4 + 1/152Babylonians YBt 365 1/(4 + (1/5 − 1/7)) 365 1/4 − 1/c.285Sudines YSt 365 1/(4 + (3 1/5)/60) 365 1/4 − 1/304———– YAg 365 1/(4 − 1/(100 + 100/60)) 365 1/4 + 3/4868———– YAg’ 365 1/(4 − 1/100) 365 1/4 + 1/1596

32 Aristarchos’ pre-Hipparchan Precession 1999 June DIO 9.1 ‡3

B2 Until the revelations to follow (below), I would say that the starkest hint of ancientuse of continued fractions was the Archimedes approximation-bracketing of π:

3 + 10/71 < π < 3 + 10/70 (1)

Why else would the variation appear in the denominator?B3 Continued fractions are the key that unlocks Table 1. If we presume that the ta-ble’s data evolved from an uncomprehending scribe’s6 copying numbers which representedcontinued-fraction expressions (in whole or in part), then we may easily find the solutionsset forth here in Table 2 (where I render the unmysterious cases also as continued fractions,just to provide extra illustrative examples).B4 At first glance, it may appear that the sign-choices are arbitrary. However, uponreflection, it is obvious that without some negative signs, all the years listed in Greeknotation would be shorter than 365d1/4 (and thus sidereal years would be unrepresentable)by the continued-fraction interpretation of Table 1. And, without some such interpretivehypothesis, the figures of Table 1 are the gibberish that Neugebauer rightly calls them.7

An obvious point: no normal Greek fractional expression used fractions in non-descendingorder of size, as in, e.g., the case of list B’s Aristarchos year, 365d1/4 1/10 1/4.B5 This case also illustrates why flexible use of plus or minus signs is efficient (and thuswould be attractive to those ancients who worked with continued fractions): if one tries toexpress 365d1/4 + 1/152 using only the usual plus signs, the result is:

365d +1

3 +1

1 +1

8 +1

1 +1

3

(2)

But simply permit sign-flexibility, and the outcome is much compacted:

365d +1

4 −1

10 −1

4

(3)

which is the expression for YAs in Table 2.B6 Anticipating the inevitable question regarding the influence of preconception, let mesay that I started investigating Table 1 in search of values for the actual tropical year Yt.[See fn 18 for real ancient tropical and sidereal yearlengths.] I never found a one. Theonly plausible tropical results instead kept coming out near the old standard (but highlyerroneous) Hipparchos-Ptolemy value (eq. 10), YHt = 365d1/4 − 1/300.

6An alternate hypothesis is that a deliberate attempt was made to disguise-encode the values of thelength of the year so that non-initiates could not understand them. The legendary secrecy of ancientscience (or pseudoscience) has been knowledgeably ridiculed by Neugebauer (op. cit., 566): “all these‘secrets’ were eagerly written down and have survived in countless copies . . . .” But the inherentsampling-completeness infirmity [DIO 4.2 ‡9 §I] of this reasoning reminds one of Count Fosco’s retortto the confident idea that crimes always out: “Yes — all the crime you know of. And what of the rest?”(Wilkie Collins, The Woman in White, 1859-1860.) Whatever the degree of success, it is undeniablethat some ancient cults treated knowledge as an elitist treasure not to be lightly shared. See, e.g., #143of The Letters of Synesius of Cyrene, English translation by A.Fitzgerald (Oxford Univ, 1926).

7See Neugebauer op. cit., p.602. Also R.Gillings Historia Mathematica, viii (1981), 456-457 onEgyptian writing of fractions (a different context, though Alexandria is geographically Egyptian):“Scribes never used signs” (brought to my attention by Owen Gingerich in 1982 February).

Aristarchos’ pre-Hipparchan Precession 1999 June DIO 9.1 ‡3 33

B7 Some of the Table 2 interpretations of Table 1’s data may look arbitrary; however,considering the relatively small number of interpretive options available, one must ask whatthe odds are on: [a] The exact appearance of two known Aristarchos (calendaric) numbers,152 (§C8) and 4868 (§C3). [Note that these numbers may be related: 32 cycles, of 152y1/8each, constitute 4868y. Note also that Hipparchos’ final lunisolar tabular epoch (DIO 1.1‡6 eq.28), −127/9/24 1/2, was 152y1/4 after Aristarchos’ −279 S.Solstice, which we knowHipparchos used to found his YHt: ibid §B4.] [b] The repeated appearance of integer-factormultiples of 76 (Kallippic), namely +1 (Euktemon), +2 (Aristarchos), −4 (Sudines).

C ComparisonsC1 For simplicity in explanation below, we set the convention that the year Y is relatedto a reciprocal remainder R (reflecting the deviation from the Kallippic-Julian year YK =365d1/4) by the easy equation:

Y = YK + R−1 = 365d1/4 + 1/R (4)

C2 The Kallippic cycle of 76y obviously figures in the Table 2 data. The Euktemonyear YE (365d+ 1/RE) exceeds YK by an accumulated total of 1d per Kallippic cycle — i.e.,RE = +76. Aristarchos’ sidereal year YAs (list B): 1d excess every 2 Kallippic cycles (or152y), i.e., RAs = +152. Sudines’ (c.240 B.C.)8 tropical year YSt: 1d defect every 4 cycles(or 304y), i.e., RSt = −304.C3 The Aristarchos tropical year YAt (list A): 1d defect every 18 Saros cycles, where weknow9 that Aristarchos’ value for the Saros was

18y10◦2/3 = (1622y2/3)/90 = 4868y/270 (5)

Thus, RAt = −18·4868/270 = −4868/15 = −324 8/15. Since the number 4868 haslong been associated with Aristarchos (see §A2, fn 11, and Neugebauer op. cit. p.603), itsappearance in Table 2 under his name is particularly striking.C4 The Babylonian sidereal year YBs (list A) shows an excess over YK (365d1/4) of 1d

every 144y, which may be a rounding of 8 Saros (about 144y.2). YBs = +144.C5 The Table 2 expression for the Chaldean (list A)-Babylonian (list B) tropical yearYBt looks over-speculative at first; however, if we presume an intent to quantify a yearwhich corresponds to a defect of 1d every 15 Metonic (19y) cycles, that is every 285y

(YBt = −285), then a continued fraction solution would be (rounding 17.5625 to 17 1/2 or

8Neugebauer op. cit., p.611 n.31.9 See fn 11 below. (Alm., IV 2 has same Saros-length as eq. 5. The Tannery-reconstructed Aristarchos

period was half of that equation’s 4868. And 2434 years Y = 30105 synodic months M = 32265anomalistic months A = 32670 draconitic months D = 32539 sidereal months. These figures use therelatively simple Saros relations (Alm., IV 2): 223M = 239A = 242D (where 242 = 2·112). It isa provocative [though far from conclusive] coincidence that the simplest fractional expression whichwill yield precisely eq. 13’s monthlength M (Alm., IV 2) is 99902/3383, where we note that 99902 =2·11·19·239. These familiar factors permit simplifying various periods via convenient cancellations:YM = 235M /19 = 235·2·11·239/3383 = 365d1/4 − 43/13532.A = 223M /239 = 223·2·11·19/3383 = 27d1873/3383.D = 223M /242 = 223·19·239/(11·3383) = 27d7892/37213.(In an age of tedious computational means, relatively short fractional expressions were preferable tolong sexagesimal ones. [Similarly: since 3383 is 17·199, cancelling 17 in the key eq.1 of DIO 6‡1 finds: 2·11·17·19·239·251/(17·199) = 126007d9/199.]) For a completely different explanationof M (also to all sexagesimal precision given in Alm., IV 2), see Noel Swerdlow, “Hipparchus’sDetermination of the Length of the Tropical Year and the Rate of Precession”, Archive for History ofExact Sciences, xxi (1980), 291-309, pp.307-308. [Also simple DR solution bracketed below at §D4.]


35/2, to avoid the lengthy exact solution):

365d1/4 − 1/285 = 365d +1

4 +1

17.5625

≈ 365d +1

4 +2

35

(6)

The ancient preference for unit fractions [& compactness] would quickly tranform the lastexpression to 365d1/(4 + (1/5 − 1/7)) — as shown in Table 2.10

C6 Attempts to solve the last item in list B of Table 1 must contend with the lacunaein data and even name. A guess is that this year might be related to the Aristarchan yearrelayed by Censorinus:

YAg = 365d1/4 + 1/1623 (7)

which Tannery reconstructed11 more exactly as

YAg = 365d1/4 + 3/4868 (8)

C7 One possible explanation of the Table 1 version is: 365d1/(4 − 1/(100 + 100/60)),which equals YAg precisely.12 Another explanation is: the nearest integral multiple ofRAg in Kallippic cycles is 21 cycles, which is 1596y , the alternate figure found in Table 2(RAg’ =1596), where it is implicitly speculated that σ′ is not a number but part of a mutilatedword on the original record list B was copied from. This value is consistent with the factthat all other years of list B have here been found to be based upon fit-roundings to theMetonic cycle (19y) or Kallippic cycle (76y = 4·19y), not the Saros.C8 The relating (in Table 2, list B) of the Aristarchos sidereal year

YAs = 365d1/4 + 1/152 (9)

(RAs = +152) to him is as definite as was the case with his tropical year (above) — sincewe know13 that Aristarchos’ 280 B.C. Summer Solstice [−279/6/26 noon]14 was exactly152y after the famous Meton 432 B.C. Summer Solstice.

10Subsequent to positing this (in the 1st draft of this paper, transmitted for me by Michael Hoskin tothe 1980 June Aristarchos conference on Samos [where it was not read]), I realized the likely originof RBt = −285. It is clear from Alm., IX 3 that [the ancients quite commonly] rounded to 60ths ofa day (i.e., one sexagesimal place) when reporting astronomical period relations. If one expresses theMetonic cycle so, it is [by eqs. 12&13] 6939d41′. Divide by 19, and one gets exactly 365d1/4 − 1/285.(Note also that 285y [underlies both Ptolemy Alm., III 1 equinox fabrications: DIO 8 ‡1 Table 1].)

11 See Heath, op. cit., pp.314-315, and Neugebauer, op. cit., pp.603-604. [It is also possible that thelast entry in List B is related to the anomalistic year. See DIO 6 ‡1 eq.6 & fn 40.]

12The precise agreement has of course been achieved only because σ′ has been arbitrarily presumedto be a scribe’s error for 100′ or 100/60. (Sole defense: the astonishing agreement with YAg.)

13Alm., III 1. [Alternate theory for Aristarchos B: 365 1/(4 − 1/(10 + 1/4)) = 365 1/4 + 1/160.If this is the right interpretation, it might be based on the −1079/6/24 eclipse. See DIO 6 ‡1 §I2.]

14 [See DIO 1.1 ‡6 eq.8. The occurrence of the actual 280 B.C. Summer Solstice was the better partof a day later. See §E3. Thus, the precise observed solstice-time may have been rounded to equal thenoon of the calendar day containing the event. See Rawlins Bull. Amer. Astron. Soc., xvii (1985), 583,where it is suggested that Aristarchos indeed truncated the observed Summer Solstice’s time to diurnalepoch-hour (noon for him) a practice that (the 1985 paper theorizes) would be a natural tradition forcalendaric astronomers since Meton — and which obviously tended to cause later astronomers (whohad to use older solstice data for computing mean yearlength) to systematically overestimate Y . Seealso DIO 1.1 ‡6 §E4.] Proximity to the Dionysios era suggests Aristarchos’ connexion to the 365d1/4Dionysios calendar, which was used [by Dionysian heliocentric astronomers: DIO 1.1 ‡1 §D] to dateeight Alm. data (3rd century B.C.), mostly observations of Mercury. We take epoch (start of Dionysiosyear 1 = Ptolemy II year 1) = −284/6/26 noon and adopt the reconstruction of August Bockh, uberdie vierjahrigen Sonnenkreise der Alten . . . (Berlin, 1863), 286-340. The lone non-fitting Alm. dateis the Mars-βSco conjunction, off by 1d — but R.Newton has found that the real conjunction was1d off the Alm. report. Thus, Bockh’s scheme seems completely vindicated. (Noon epoch is myspeculation [based on noon’s diurnal analogy to the Summer Solstice’s annual effect].) I suspect thatthe 280 B.C. observation was taken to help establish the Dionysios calendar. By this scenario, the1h-precise observed time is now lost (and was not even known to Hipparchos or Ptolemy).


C9 Both this value and the Babylonian sidereal year YBs (RBs = +144) are close to thatof the tables of the Almajest (where RPs = +147)15 and to the actual16 sidereal year Ys ofthat epoch, when Rs = + 153.C10 Notice that all the tropical years of Table 2 (YAt, YSt, YBt) are very erroneousyet all are quite near the rounded value later used17 by Hipparchos and Ptolemy, eq. 10.And RHt = −300, whereas actual18 Rt = −133 in [the former’s era, becoming −132 byPtolemy’s time].

D Conclusions

What do we learn from the foregoing?D1 Table 1 is the oldest extant material expressed in continued-fraction format, albeitcorruptly.D2 The veil has been pulled aside from a flock of long-lost ancient values for the lengthof the year.D3 The sidereal-year estimates (Ys), being strictly astronomers’ values, are unforcedto civil considerations. [Which is part of the reason that ancients’ Ys are so much moreaccurate than their Yt.] These Ys values are probably based [see, e.g., Rawlins, Vistasin Astronomy xxvii (1985), 255-268 §5, also DIO 6 ‡1] upon lunar eclipse observations,which do not require high precision visual measurements to determine Ys to good accuracy.[See DIO 1.1 ‡6 fn 1.] As seen above, Aristarchos’ value, YAs, is astonishingly accurate(RAs = 152 vs. actual Rs = 153 for his epoch), correct to a few time-seconds. However, thisproximity may be much an accident of rounding.

15Perhaps RPs = +147 was also Hipparchos’ value. However, there is evidence that he used thenearby value, RBs = +144. See Neugebauer, op. cit., 293, and Swerdlow, op. cit., 300. [See alsoDIO 6 ‡1 §C.]

16 This figure includes both the secular variation of the Earth’s revolution about the Sun and [thegreater (but oft-ignored)] effect of the Earth’s spin acceleration [DIO 6 ‡1 fn 53] upon the length ofthe day itself. [(Gingerich 1981 Q. Jl Roy. astr. Soc. 22:44 ignores both.) See also fn 18. It issometimes helpful to have at-hand rough values for the accumulated effect; so, accurate to ordmag10m, I give ∆T (and the Besselian date) for each of several calendar epochs: Meton (−430.527) 4h,Kallippos (−328.525) 3h3/4, Dionysios-Aristarchos (−283.527) 3h1/2, Hipparchos (−126.278) 3h,Antoninus-Ptolemy (+137.547) 2h1/4. Since empirical estimates of Y were based on data extendingbackwards in time, the apt Rs for comparisons would be a little less than that for the astronomer’s ownera. For Aristarchos, we make no adjustment, since Rs was likely on the high side of 153 in 280 BC.]

17 Alm., III 1 — though Censorinus (Heath op. cit., 297) rendered Hipparchos’ year as 365d1/4 −1/304 (which is YSt of Table 2).

18 See fn 16. [Rs & Rt are obviously not exact. Each is figured for the era of Aristarchos androunded to the nearest integer, being uncertain by a few tenths of a unit in the last place. (Both figuresgrow more positive in time, roughly 2 units/millennium, sidereal rather more slowly than tropical.)Note that the most applicable R — that for Summer Solstices — is not really −133 (a value basedupon mean solar motion) but is instead −124. (So the ancients’ values [§D4] were even farther fromempirical truth than is indicated by superficial analysis.) This is because all knowledgeable ancientsused Summer Solstices to gauge yearlength Y . (See fn 25.) It is seldom appreciated by moderninvestigators that (due to the variation of eccentricity & apse in the Earth’s orbit) each seasonal eventhas its own yearlength Y (differing from the others by ordmag 1m) and so (by eq. 4) its own R. I hereprovide these for 280 BC: S.Solstice Rt = −124; A.Equinox Rt = −138; W.Solstice Rt = −144;V.Equinox Rt = −129. (The harmonic mean of opposite values of course yields −133 for each pair.)The sidereal year will also differ from star to star, around the zodiac. (And Ys’s periodic variation, as afunction of chosen zero-point longitude, will be similar to Yt’s.) So our analyses here of Rs implicitlyassume a broad enough ancient observational data-base, that mean solar sidereal motion was beingmeasured.]


D4 Ancients’ estimates of the tropical year (Yt) ought to have been based upon centuriesof high-precision transit observations.19 However, the tropical year was the civil andreligious year, in an age of strong traditional reliance on lunar calendars. Thus, TobiasMayer long ago suggested20 that Hipparchos’ yearlength,

YHt = 365d1/4 − 1/300 (10)

(6m too long), was based on a fit to the Kallippic cycle (established 330 B.C.) relatingtropical (civil) years Y to synodic (civil) months M , by defining a Metonic year YM fromthe lunisolar equation

76Y = 940M (11)

which is the same ratio as the older Metonic cycle (established 432B.C.),

19YM = 235M (12)

The length of the month had become [DIO 1.1 ‡6 fn 1] very well established by Aristarchos’time at the excellent estimate:

M = 29d; 31, 50, 08, 20 (13)

(accurate to well within 1s, both in antiquity AND today). [DIO loc. cit. speculates thathe was responsible for determining this famous value — by the extremely simple methodexplained at DIO 6 ‡1 §A5 & fn 18.] So the [Metonic “year”] was

235M/19 = 365d1/4 − 1/315 (14)

i.e., RM = −315 very nearly. That Mayer’s theory is no longer just a speculation may bediscerned from the tight cluster of tropical year values Table 2 has showered upon us all atonce; adding21 in already-wellknown YHt (eq. 10), we have the following tropical Rt values:RBt = −285, RHt = −300, RSt = −304, RAt = −324 8/15. All four are very near theMayer-Metonic calendaric-numerological value, RM = −315, and all four are very far fromthe correct ancient value, Rt = −133 [actually −124: fn 18]. As we have already seen,each astronomer rounded in a different fashion (using, e.g., 1st or 2nd place sexagesimalroundings en route to Yt, or rounding Rt to the nearest multiple of Metonic, Kallippic, orSaros cycles, or centuries). But obviously all shared the a priori prejudice that Rt = 315(or some nearby transformation of it) was about right. [Even accounting for the systematiceffect noted at fn 14], it is impossible to believe that all 4 of the Rt values just reprised(−285, −300, −304, −324 8/15) were based upon independent solar observations that justhappened by chance to arrive in the vicinity of the same (very wrong) lunar-based (eq. 14)value, RM = −315. A classic contrast of numerological forcing vs. what was to be expectedfrom [neutral] empirical observation (Rt = −133). The overwhelming vindication here ofMayer’s supposition ensures that we now know the source of the wellknown +6m error inYt — which accumulated [(DIO 8 ‡1 �1) to 26h] in the interval between the solar theories

19 Transit-observations of ordmag 1′ accuracy were within the capability of some ancient astronomers.See Alm., I 12 [also Rawlins 1982 (of fn 3) n.17, and Rawlins 1985 (of §D3) §§3&5.]

20 Swerdlow op. cit., 292; other scholars ([including Swerdlow and] myself) have since rediscoveredMayer’s finding, primarily Kristian Moesgaard and Raymond Mercier (see ibid 293), contra R.Newton.

21Swerdlow (ibid., 292) suggests that RSt = −304 (fn 17, above) might have been rounded toRHt = −300 via a rounding of a Kallippic cycle of 940M to 27758d45′, followed by a 2nd-sexagesimal-place rounding of a 76th of the result, which would indeed give 365d14′48′′ (Alm., III1). [This speculative reconstruction is not at all impossible (similar discussion on rounding at DIO 1.3fn 274);] but without the 1st rounding, the upshot would’ve been 365d14′49′′, thus R ≈ −327≈ RAt = −324 8/15 (Table 2 list A). Alternate theory: 432 B.C. to 135 B.C. ≈ 300y (fn 14 above).


of Hipparchos (c.−130) and Ptolemy [whose date is almost irrelevant here, since all of hisalleged +132-140 AD solar “observations” were faked], producing the infamous solar meanlongitude error (over 1◦, negative) that infected all of Ptolemy’s tables (the fundamentalastronomy for which was borrowed entirely from Hipparchos) — the fatal error whichultimately revealed the truth behind Ptolemy’s pretense that he was a regular observer ofthe sky.22

D5 Annual precession p (the difference between the sidereal and tropical years) [wasunderstood by Aristarchos, though not by Meton or even Kallippos (who proposed only oneyearlength each), so Aristarchos was the earliest known scientist to recognize precession.The difference was also evidently (Table 2) accounted for by Babylonians — who are, wenote, listed later than Aristarchos, in chronologically-ordered Table 1. (See DIO 1.1 ‡6§§B11-B13.) Aristarchos gauged p ] at very nearly 0◦.01 (or 0d.01) per year (in rough terms:1/150 + 1/300 = 1/100), the mistaken figure adopted over a century later by Hipparchos(hitherto universally credited with the discovery of precession). We may even deriveexact figures for these early precession values by using the following equation for findingcentennial precession P :

P = 100(360◦/Y )(Ys − Yt) (15)

From this and the numbers developed in this paper, we find for Aristarchos [whose YAs &YAt in Table 2 are fortunately the firmest decipherments there]

PA = 100(360◦/Y ) · (1/152 − [−1/(324 8/15)]) = 0◦.952 (16)

and for Babylonia:

PB = 100(360◦/Y ) · (1/144 − [−1/285]) = 1◦.03 (17)

— both deduced values being close to that of Hipparchos-Ptolemy [PH = 1◦.00], but farfrom the truth for antiquity (1◦.38).

E Prejudices [The Part Totally Suppressed by Hoskin]E1 Hipparchos’ lack of originality in his tropical year (eq. 10) and his centennial pre-cession of PH = 1◦, should not entirely surprise us.23

E2 However, to forestall potential misunderstandings of the implications of this paper,I must here stress that there is little comparison between his failings and Ptolemy’s withrespect to the issue of non-originality.E3 His month (eq. 13) was accurate (thus agreement is not suspicious — his ownresearches indicated a trivially different value).24 His YHt was based upon a comparisonof solstices (wiser than using equinoxes):25 his own −134/6/26 1/4 Summer Solstice[error −1h] and Aristarchos’ −279/6/27 1/2 Summer Solstice [error −16h] (The total+15h error26 of the time-difference, for 1 1/2 centuries, led directly to the fateful error

22See fn 29 below. Perhaps the most obvious proof that Ptolemy was not a regular observer is thesimple fact that he did not know his own alleged observatory’s latitude! (Alm.,V 12-13 — an error of−14′.) [See Rawlins 1987 (of §E3) p.236 item (2).]

23[See, e.g., DIO 1.3 §N16.]24Alm., IV 2. Note that use of lunar eclipses for finding the synodic month and the sidereal year

allows far greater accuracy (from modest visual work) than the use of solar transit observations (Alm.,I 12 and III 1) allows for the determination of the tropical year (see above at §§D3&refsec-aD4). SeeRawlins (of §D3); also DIO 6 ‡1.

25 See R.Newton, Crime of Claudius Ptolemy (Johns Hopkins Univ, 1977), 81-82 and 85-86. AlsoRawlins here at fn 14 [and at DIO 1.1 ‡5 fn 20].

26See fnn 14&16, above.


in YHt: 0h.1 = +6m.) Hipparchos could be faulted for (probably [see DIO 1.1 ‡6 §E5])prejudiced selection of the required ancient-to-him [S.Solstice] (Aristarchos’), but nothingmore. His own solstice’s error was trivial. (Aristarchos’ was not. [For cause, see fn 14.])Hipparchos’ 21 [extant] solar observations are of fair accuracy (rms error 8h) — normalrandom and systematic27 errors. By contrast, Ptolemy’s 4 solar “observations”, which agreewith Hipparchan data to within less than a half-hour in all cases, disagree with reality by[21h, 33h (twice), and 36h]. The Ptolemaic data’s [31h] rms deviation from reality is over50 times [their 0h.6 rms] deviation from Hipparchos’ solar tables. For Hipparchos himself,this ratio is only about 2 (instead of 50+) and even much of that is due to the fact thatof course his tables were fit to his observations. [Thus, the common blanket-slander thatancient scientists were non-empirical is simply one more Hist.sci-establishment fantasy.See Rawlins, Amer. J. Physics, lv (1987), 235-239, n.12. See also fn 19 here.] (Even so,Ptolemy’s “observations” adhere 5 times more closely to Hipparchos’ tables than do theHipparchan observations on which the tables were founded!)E4 The point to keep in mind here is that whereas gauging the year entails dependenceupon a predecessor’s work (e.g., Hipparchos’ use of Aristarchos’), finding solar positionshas no such dependence. (Thus, the impact of the above-cited ratios.) The reality ofHipparchos’ data for position is clear from a glance at his solar theory: despite its fallaciousyear-length (mean motion), its longitude-at-epoch is very close to the truth for his own time.[See DIO 1.1 ‡6 §D7.] On the other hand, all of Ptolemy’s positional “observations” areconsistent with this same theory — a theory that gave correct positions only for Hipparchos’time, but was slow by over 1◦ by Ptolemy’s epoch.28

E5 R.Newton’s analyses of Ptolemy’s data (especially solar and stellar)29 have con-cluded that he was not simply prejudiced but that he systematically deceived (to highprecision) in support of these prejudices. Newton’s conclusion has been attacked with suchpassionate disbelief in a variety of journals (by commentators all whom had, in earlierpublications, prejudged Ptolemy as a great astronomer), that many onlookers may not beaware that a number of scholars agree that Ptolemy has indeed been shown to have been aliar. These include B. L. van der Waerden and myself.

Acknowledgements

I thank Willy Hartner and Kristian Moesgaard for their useful comments upon the prelimi-nary (1980/6/15) draft of this paper, and Robert Newton for his helpful advice on the 1981draft.

27All of Hipparchos’ Vernal Equinoxes are a few hours early; all his Autumnal Equinoxes are a fewhours late. (This is perfectly consistent with his transit instrument’s equator having been set a fewarcminutes low. [But see the attractive alternate theory implicit in Swerdlow’s proposed Hipparchossolar parallax: DIO 1.3 fn 280.]) By contrast, all of Ptolemy’s equinoxes (Vernal and Autumnal)are late. (Very. The smallest of Ptolemy’s three Equinox errors exceeds the largest of Hipparchos’twenty Equinox errors — Ptolemy’s rms error was 4 times Hipparchos’.) This circumstance cannotbe explained by misplacement of the transit instrument, which Ptolemy says he used, Alm., III 1(unambiguous ref. to Alm., I 12; see R.Newton, “Comments on ‘Was Ptolemy a Fraud?’ . . . ”, Q. Jl.Roy. astr. Soc., xxi (1980), 388-399, pp.389-390).

28This is illustrated, to devastating effect, by Raymond Mercier at p.215 of British Journal for theHistory of Science, xii (1979) 211-217, his review of R.Newton, Ancient Planetary Observations . . .(Johns Hopkins Univ, 1976). Note too that almost all of “Ptolemy’s” Alm. tables end in 82 AD [a factfirst broadcast by A.Rome] .

29 See R.Newton, opera cit (fnn 14, 25, & 29) and “On the Fractions of Degrees in an Ancient StarCatalog”, Q. Jl. Roy. astr. Soc., xx (1979), 383-394; also Owen Gingerich, “Ptolemy Revisited . . .”, Q.Jl. Roy. astr. Soc., xxii (1981), 40-44, p.42.


F JHA Editorial Integrity. Again . . . . [Note Added 1999 Dec]F1 The foregoing is the paper long referred to (semi-facetiously at first) as “Rawlins1999”, in numerous articles appearing in this journal. (Some of the history of its persistentsuppression was previously recounted at DIO 1.2 §B2 & fn 9.)F2 Since the paper’s main math opposed (fn 20) a specific R.Newton contention, OwenGingerich encouraged the expansion of a brief 1980 version of it for publication in the Jour-nal for the History of Astronomy. Almost two decades ago, this was submitted (1981/8/7)in the version printed here at §§A-E and was promptly accepted30 (1981/9/17) by JHAEditor Michael Hoskin. However, the 1981 version ended with a section (§E) that de-fended Newton’s general view. In retrospect, it is obvious that the JHA wanted only theanti-Newton part — but didn’t want to say so. Thus, there ensued a ridiculous series ofpublication-postponements (during which time the paper could have been before an honestjournal), accompanied by increasingly thespian expressions of sorrowful apology.F3 DR repeatedly inquired as to whether the content was a problem. Consistent denialsof this (indicating JHA reluctance to appear censorial, evidently hoping that enough delaymight push DR into angry withdrawal of the paper, thereby neatly solving the JHA’stheological dilemma) were followed by a sudden 1982/7/27 demand for immediate DRassent to a version chopping off the concluding section (the pro-Newton part: §E above),which had committed the special sin of pointing out (what the JHA was loathe to reveal)that some reputable scholars such as van der Waerden (fn 34) did not agree with the JHAcrowd’s rejection of Johns Hopkins Univ physicist Robert Newton’s recent charges thatPtolemy was a liar. The JHA continues to imitate its hero’s ethics in its private explanationsof this incident. (See DIO 1.2 §B1. The attendant ugliness, false slander, and censorshipled ultimately to the birth of DIO.) [In 2002, JHA’s smear was published nationally. SeeDIO 11.1 p.2.]F4 The JHA has quite recently shown that its integrity has not changed: it continuesto dishonor its own original agreement to publish the full paper, as it even today insiststhat §E5 must be censored. Disturbed that the paper’s remarkable results were being keptpermanently from the academic community, and increasingly convinced (by the behaviordescribed below) that the JHA would exercise interminably its idea of high creativity bycontinuing to find some excuse or other to impede the prospect of publication (therebythrowing away a perfect opportunity for that journal to improve relations with DIO — and,more important, to demonstrate the large-minded universality to which it seems to aspire),DR has decided to publish here in DIO the unbowdlerized paper.F5 Readers who expect (hope?) to be shocked at the original prose will be badly letdown. The true shock here is how afraid and one-sided the JHA continues to be. It cannotprint any paper that says in so many words that Ptolemy was a liar. [But: no-problemfor papers opposing that view; see, e.g., §F8.] It cannot even admit that there is a seriouscontroversy about whether he was. (Check for yourself what the JHA finds so hideouslyoffensive at §E5.) Instead of falsely laying blame (§F6) on others, for a problem that aroseentirely because of its own intellectual and ethical limitations, the JHA might considersurprising its critics (e.g., DIO 4.3 ‡15 §H10), by rethinking its goals, and reflecting onhow the devil it became so politically narrow that it would actually suppress key new findings

30DR had even gone to the trouble of putting the paper into the JHA’s inexplicably-preferred style.Some of the additions to it here are done DIO’s way; thus the odd mix of styles in the present version.The paper has been improved and augmented here&there. Serious additions are in brackets. None ofthese alterations have anything to do with the offending sentence in §E5.


(certified as such by both of its own eminent referees)31 and for years hold these resultshostage to an insistence that DR betray an honest scholar (R.Newton) and the obvious truth— and consent to join in the JHA’s obsessive decades-long try at misleading academeregarding the state of the Ptolemy controversy. (How can Hist.sci be taken seriously as adiscipline, when one of its most prominent journals resembles a church? — banning ideas,even researchers. When did the Hist.sci community begin uncomplainingly taking it forgranted — as an enduring & unalterable Reality — that a politically prominent academicjournal will rigidly promote a certain viewpoint, boosting only one side of a controversywhile handicapping another?)F6 A good start at reform here would be a retraction of the behind-the-back falsehood(DIO 1.2 §B1) that DR was “impossible to deal with” regarding the present paper. (Checkidem or here at fn 31 to see just how perversely opposite the actuality was.) Severalyears ago DR warned in DIO that (with the millennium ending), the paper’s increasingly-unhumorous tag as “Rawlins 1999” meant that time was running out for Hoskin to “fulfillhis written agreement” (DIO 6 ‡3 fn 24) to publish the paper. Honest Hoskin made noreply. (Since DIO began, Hoskin has just mailed back all issues, unopened. He thinks thisproves something. And it does. Question: Is anyone in the Hist.sci community concernedat what is done to the reputation of academe, when the publisher of the leading Britishjournal for astronomical history refuses to communicate with his US counterpart? For over16 years now.)F7 With 1999 passing, and while there seemed to be growing hope32 of encouragingpeace, mutual tolerance, and open discourse between the formerly warring camps andjournals, DR asked JHA-Number-Two-Leader about the “on-ice” paper (as he had come to

31 The paper was submitted in final form 1981/8/7. Hoskin soon reported (1981/9/17) that the“paper is accepted in principle but we need to work at getting your message across to the reader.Moesgaard has very kindly agreed to try his hand at a draft modified version for your considerationand I hope to send this to you in a few weeks.” (Emph added.) The referees were Willy Hartner &K.P.Moesgaard. Hartner had (after initially nixing the paper) directly informed DR of his positiveverdict on 1980/8/15, but Moesgaard’s prompt referee report on the 1981 version was long heldprivate — even when its content was requested. The report recommended that the paper be softened.(Readers here of the original 1981/8/7 DR version [keeping in mind that brackets indicate post-1981changes & interpolations] can now judge for themselves the validity and purpose of that suggestion.)This intent was kept private for a half-year — despite DR’s direct 1981/11/27 questions about whatMoesgaard was to do. Instead of imparting his plans, Hoskin denied to DR that any tampering withthe content was to occur (a denial Hoskin maintained right up to the 1982/7/27 moment when theJHA rush-demanded tampering, and simultaneously relayed Moesgaard’s report at last). After DRoffered in late 1981 to have a friend (the former Editor of the American Geographical Society) do theever-elusive clarity-enhancing revision, that was allegedly delaying the paper month after inexplicablemonth, Hoskin declined, saying (1981/12/27): “It’s totally a matter of making the message clearer tothe reader. That’s all.” And: “The paper won’t present any problems. . . . everything’s OK and there’sno problem. And you’ll be hearing from me within the next month.” More months passed, along withtwo more apologies. (E.g., “especially to apologize for my delay in revising your paper & to thankyou for your patience. It must certainly go in the October issue . . . . Many apologies!”) DR treatedHoskin with such extreme politeness throughout this charade that it bordered on obsequiousness. DRactually offered (seriously) to visit Cambridge to assist the work of revision; Hoskin declined the help,but replied (1982/5/30, emph added): “I feel very guilty about this. It’s simply a pressure of otherthings. . . . it’s nothing more than that . . . . You’ve been extraordinarily patient. . . . again my thanksfor your patience.”

32 See inside cover of this issue. Also, the JHA had in 1998 published (without the slightestinterference) John Britton’s erudite torching (JHA 29:381-385) of the gas in Swerdlow’s 1998 P.U.book, though Swerdlow is one of the JHA’s “Advisory Editors”. And a paper from Russia (an earlierversion of which was commended at DIO 4.3 ‡14 fn 4) giving evidence for Hipparchan authorshipof the Ancient Star Catalog is said to be in the offing at JHA. One hopes that the authors will not becajoled into warping the logical conclusions of their own research — as has happened in the recentpast in Hist.sci. (See, e.g., DIO 1.2 §I8. Process satirized [barely] at DIO 6 ‡3 fn 11.)


call it). He said (1999/7/3) that THE problem with the paper was a single terrible sentence— though he couldn’t quite remember what it was. Unable at first to find his originalcopy, he wrote DR, carefully attempting to commit the JHA to nothing (forgetting that anhonest journal would already be committed, after it had thoroughly refereed and acceptedthe paper — especially in light of Hoskin’s airs about being bound by referees’ advice,whenever this suits JHA’s wants). Number Two said (1999/10/7, emph added): “I wouldcertainly be willing to urge a reconsideration of [the paper] upon receipt of a clean copyof it with the offending sentence removed.” (This is an important clarifier of what hadoriginally gone on behind the scenes, because Hoskin had never even been frank enoughto admit that this sentence was the problem. He’d originally gotten rid of the sentence byjust wide-broom-sweeping-out the whole pro-Newton section [§E] that included it.) DRsent along a photocopy of the paper, knowing that no sentence in it was improper — andtherefore challenging Number Two to find such (1999/10/15): “I look forward to learningwhat the intolerable sentence in it is.” Reading the paper, Number Two soon learned thatno sentence in it could be defensibly condemned. He then dug out his original 1981 copy— but still found no impossible sentence. So, he shifted to a new ploy: he excerpted justa portion, a phrase, from the sentence in question! — and used that as an excuse to keepon33 arguing for censorship (1999/10/25): “You will not have a ghost of a chance of gettingyour paper published in the JHA as long as it contains the phrase [at §E5] ‘that Ptolemy hasindeed been shown to have been a liar’ ”. However, the full sentence is not a claim of proof(as the excerpting makes it sound), but is rather a description of the Hist.sci sociologicalsituation on the issue. (Must the JHA mutilate a sentence, in the cause of mutilating thejournalistic truth of its attempted mutilation of an article on a long-mutilated historical

33 Hmmm. Why does such censorship mean so much to the JHA?Is the intent to aggravate DR until co-existence breaks down? (And then blame the result on him?)Or is the JHA just now so deeply into this wringer that it thinks it must resort to any available meansof conjuring up a non-existent problem with the paper, because the journal can’t admit that it neverhad cause to censor this article in the 1st place? Keep in mind that Hoskin’s 1983 severance ofcommunication with DR was caused not by the paper’s contents but by DR’s openly — not behindHoskin’s back — and gently (note old-proverb at DIO 1.2 p.96) pointing out the JHA’s poor refereeing ofa miscomputed paper it published late in 1982 (DIO 1.2 §B2 & fn 8). But the heaviest underlying factorbehind JHA censorship of the DR paper is elementary: keeping control of centrist-forum discussion ofthe Ptolemy-as-liar issue can be accomplished by the simple scheme noted at DIO 2.1 ‡3 fn 8: “tapeone side’s mouth shut.” For the unfettered other side, see here at §F8; see also the gratuitous false attackon Newton’s character (pointed out by Thurston at DIO 8 ‡4 §A19), appearing in a 1998 book that wasvetted and aggressively promoted by two JHA archons. [Remainder of note added 2000 Jan.] Thisattack is in fact based upon 1993 remarks first appearing in the JHA itself: “Newton’s arguments werebased on apparently dispassionate statistical tests, but the concluding sections of the book [Crime 1977]were marked by a personal animosity of surprising intensity toward Ptolemy” (JHA 24:145). Note thatneither of these JHA-inspired attacks on Newton’s character (& of course his competence — it doesn’tget any more ironic) has given us any quotes whatever from a pure-JHA-fantasy hatemonger-Newton,to justify JHA’s charge of “personal animosity”. I.e., this is simply more JHA smearing of Newton,intended to convince the reader that Ptolemy’s fraudulence is nothing but the figment of a lone (§F8)nut’s enraged & unbalanced imagination — when the sharply ironic truth is that the mirrorlessly-projecting JHA is itself the party whose undeniable personal animosity is doing the imagining. No onehas ever presented any evidence to support the lie that Newton’s work was motivated by personal anger— though dislike of massive cheating wouldn’t merit condemnation, anyhow — or was (ibid p.146)“ahistorical”, except insofar as the JHA (again the actual fantasizer here) megalomaniacally supposesthat it blesses its lessers by defining for them what is and isn’t legitimate history. (The JHA’s centralhistorical Principles [!] are ever so solemnly set forth at JHA 11.2:145; 1980 June; reactive commentsat DIO 2.1 ‡3 §B2.) While Newton presented proof after proof (see H.Thurston’s summation at DIO 8‡1) of his theory of Ptolemy’s character — which is a legitimate and major science-history question(fn 34, contra DIO 2.1 ‡3 §B7) — no proof at all is required by the JHA whenever the urge seizes itto trash Newton’s character again. For the explicit smear-’em-back logic that governs the JHA circle’sbehavior in this controversy, see DIO 2.1 ‡2 §H17.


truth? See ‡1 fn 10.) The actual, entire §E5 sentence: “Newton’s conclusion has beenattacked with such passionate disbelief in a variety of journals (by commentators all whomhad, in earlier publications, prejudged Ptolemy as a great astronomer), that many onlookersmay not be aware that a number of scholars34 agree that Ptolemy has indeed been shown tohave been a liar.” That’s a very different statement than is indicated by the snippet-phrase.F8 So: does the even-handed JHA stifle all scholars who try to describe in its pages whatthe academic community thinks about the issue of whether Ptolemy was a liar? Welllllll —no. And certainly not if a scholar is “safe” — i.e., can be trusted to conclude in favor ofthe JHA’s two granite religious tenets in this connection: [a] Ptolemy was not (provably)dishonest, and [b] Reputable academic consensus agrees. E.g., in a book review, the JHA’smost servile pawn on the Ptolemy debate, is permitted to discuss the very same issue —general academic opinion on Ptolemy’s lying — which the (rather more important) abovepaper was long suppressed for mentioning! His comment at JHA 24:145 (1993): “Newtondenounced Ptolemy as a liar and a plagiarist, and called into question his competence asastronomer and mathematician. . . . Very few historians have accepted Newton’s conclusionsin their entirety.”F9 We conclude with questions which deserve provident consideration.Question 1. What should we think of a journal that would ever-so-deftly35 resort (whilesuppressing vital research) to excision-sleight and inequitably-applied pseudo-rules — as ameans of convincing onlookers that it is (of all things!) playing fair with contributors?Question 2. Do any of the JHA’s decorative “Advisory Editors” or its occasional high-quality contributors36 even care?

[Note added 2001: In the foregoing, there lurks (at §B7) yet another precise appearanceof the Aristarchan number 4868. (This one was missed by all previous scholars, includingtwo decades of DR’s own researches.) Simply check the number of years between Meton’sfamous bedrock −431 Summer Solstice and the Hipparchos Ultimate-Orbit epoch −127Autumn Equinox: it’s 304y1/4. This number is exactly one sixteenth the number of years inthe “Great Year” (fn 9 & §A2) of Aristarchos. That is, the Meton-Hipparchos epoch-intervalis 4868y/16 — on the nose.]

[Note added 2013: The full, astonishingly extensive Aristarchan-Hipparchan geometric-series context, into which 304y1/4 neatly dovetails, is set forth at DIO 11.1 ‡1 fnn 14, 16,& 17.]

34 One of these scholars was the great B. L. van der Waerden. Before concluding (in his final book,1988) that Ptolemy lied (see also DIO 1.1 ‡6 fn 37), a previously neutral van der Waerden was shockedthat O.Pedersen’s otherwise valuable 1974 book on Ptolemy had not even dealt with the issue; van derWaerden commented in Annals of Science 32.6:603 [1975]: “the question of whether Ptolemy was aliar is important for everyone who wishes to appreciate the value of Ptolemy’s work. Pedersen does noteven tell the reader that Ptolemy’s sincerity has been doubted by serious scholars, and that extensivecalculations have been made to check his statements.” (Similar defense tactics discussed at DIO 4.3‡15 §§D2&D7.)

35Shades of the ineptitude of another of History-of-science’s anti-DR censorial moves (by RobertKargon), described at DIO 2.1 inside cover. (Note: DIO has since been restored to the library shelvesat Johns Hopkins University.)

36R.Stephenson is both.

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Keith Pickering [navigation, exploration, computers, science ethics], Analysts InternationalCorporation, 3601 W. 76th Str., Suite 200, Minneapolis MN 55435; tel 952-955-3179.

E. Myles Standish [positional & dynamical astronomy], Jet Propulsion Laboratory 301-150,Cal Tech, 4800 Oak Grove Drive, Pasadena, CA 91109-8099; tel 818-354-3959.

F. Richard Stephenson [ancient eclipses, ∆T secular behavior], Department of Physics,University of Durham, Durham DH1 3LE, UK; tel (44) 191-374-2153.

Hugh Thurston [early astronomy, WW2 cryptography] (Univ. Brit. Columbia, Prof. Emer.Math), Unit 3 12951, 17th Ave, S.Surrey, B.C., Canada V4A 8T7; tel 604-531-8716.

Christopher B. F. Walker [Mesopotamian astronomy], Dep’t of Western Asiatic Antiquities,British Museum, Great Russell Street, London WC1B 3DG, UK; tel (44) 171-323-8382.

c©1999 DIO Inc. ISSN 1041-5440. This printing: 2015\9\20.

A Fresh Science-History Journal: Cost-Free to Major Libraries

Telephone 410-889-1414 DIO [email protected]

DIO — The International Journal of Scientific History.Deeply funded. Mail costs fully covered. No page charges. Offprints free.

• Since 1991 inception, has gone without fee to leading scholars & libraries.• Contributors include world authorities in their respective fields, experts at, e.g., JohnsHopkins University, Cal Tech, Cambridge University, University of London.• Publisher & journal cited (1996 May 9) in New York Times p.1 analysis of his discov-ery of data exploding Richard Byrd’s 1926 North Pole fraud. [DIO vol.4.] Full reportco-published by University of Cambridge (2000) and DIO [vol.10], triggering HistoryChannel 2000&2001 recognition of Amundsen’s double pole-priority. New photographicproof ending Mt.McKinley fake [DIO vol.7]: cited basis of 1998/11/26 New York Timesp.1 announcement. Nature 2000/11/16 cover article pyramid-orientation theory: DIO-corrected-recomputed, Nature 2001/8/16. Vindicating DR longtime Neptune-affair chargesof planet-theft and file-theft: Scientific American 2004 December credits DIO [vols.2-9].DIO-opposites mentality explored: NYTimes Science 2009/9/8 [nytimes.com/tierneylab].• Journal is published primarily for universities’ and scientific institutions’ collections;among subscribers by request are libraries at: US Naval Observatory, Cal Tech, Cornell,Johns Hopkins, Oxford & Cambridge, Royal Astronomical Society, British Museum, RoyalObservatory (Scotland), the Russian State Library, the International Centre for TheoreticalPhysics (Trieste), and the universities of Chicago, Toronto, London, Munich, Gottingen,Copenhagen, Stockholm, Tartu, Amsterdam, Liege, Ljubljana, Bologna, Canterbury (NZ).• New findings on ancient heliocentrists, pre-Hipparchos precession, Mayan eclipse math,Columbus’ landfall, Comet Halley apparitions, Peary’s fictional Crocker Land.• Entire DIO vol.3 devoted to 1st critical edition of Tycho’s legendary 1004-star catalog.• Investigations of science hoaxes of the −1st, +2nd, 16th, 19th, and 20th centuries.

Paul Forman (History of Physics, Smithsonian Institution): “DIO is delightful!”E. Myles Standish (prime creator of the solar, lunar, & planetary ephemerides for the pre-

eminent annual Astronomical Almanac of the US Naval Observatory & Royal GreenwichObservatory; recent Chair of American Astronomical Society’s Division on DynamicalAstronomy): “a truly intriguing forum, dealing with a variety of subjects, presented oftenwith [its] unique brand of humor, but always with strict adherence to a rigid code of scientificethics. . . . [and] without pre-conceived biases . . . . [an] ambitious and valuable journal.”

B. L. van der Waerden (world-renowned University of Zurich mathematician), on DIO’sdemonstration that Babylonian tablet BM 55555 (100 BC) used Greek data: “marvellous.”(Explicitly due to this theory, BM 55555 has gone on permanent British Museum display.)

Rob’t Headland (Scott Polar Research Institute, Cambridge University): Byrd’s 1926latitude-exaggeration has long been suspected, but DIO’s 1996 find “has clinched it.”

Hugh Thurston (MA, PhD mathematics, Cambridge University; author of highly ac-claimed Early Astronomy, Springer-Verlag 1994): “DIO is fascinating. With . . . mathe-matical competence, . . . judicious historical perspective, [&] inductive ingenuity, . . . [DIO]has solved . . . problems in early astronomy that have resisted attack for centuries . . . .”

Annals of Science (1996 July), reviewing DIO vol.3 (Tycho star catalog): “a thoroughwork . . . . extensive [least-squares] error analysis . . . demonstrates [Tycho star-position]accuracy . . . much better than is generally assumed . . . . excellent investigation”.

British Society for the History of Mathematics (Newsletter 1993 Spring): “fearless . . . .[on] the operation of structures of [academic] power & influence . . . much recommendedto [readers] bored with . . . the more prominent public journals, or open to the possibilityof scholars being motivated by other considerations than the pursuit of objective truth.”

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